Diagnosis of abnormal conditions of an aerobic SBR process

Abstract

Process fault diagnosis (PFD) allows a control system to maintain the operation of a process under the presence of faults. This is a critical feature for a discontinuous activated sludge waste water treatment (WWT) process in a sequencing batch reactor (SBR), treating waste water contaminated with organic toxic compounds. Here, a methodology for diagnosis based on the extraction of characteristics from the respiration signal, a known indicator for biological activity in aerobic WWT processes, and their classification is proposed. The usefulness of the signal for the detection and classification of a set of defined abnormal conditions was verified through sensitivity analysis. The analysis not only shows the effects of parameter deviations but also indicates the characteristics to be extracted from the respiration signal for a successful classification. Results obtained by simulation indicate that the signal based PFD can successfully cope with uncertainties common in this type of bioprocesses, which prevent the straightforward application of analytical PFD approaches.

Keywords:

• fault detection and isolation
• signal analysis
• classification
• sensitivity theory
• aerobic batch process

1. Introduction

Sequencing batch reactors (SBR) for waste water treatment (WWT) based on the fill-and-draw principle 1 are commonly employed to deal with variations in flow and composition of residual waters 2. For autonomous operation, these batch processes require a control system that maintains the operation even under the presence of faults. To achieve this goal, the process has to be permanently monitored to detect the presence of faults, diagnose their type and size 3, and take corresponding actions. Different authors 4-8 have presented a large variety of methods for process fault diagnosis (PFD) with examples from different areas. Nonetheless, given the uncertainties of the quantitative models used to describe WWT processes, recent publications 9-12 indicate a tendency towards application of methods from the area of artificial intelligence (AI) and statistics for the detection and isolation of process faults. Many of these data based PFD methods make use of feature extraction and classification, where the diagnosis is obtained from a classification model that is created from knowledge extracted from historical process data and diagnostic information. The difference between the various methods is marked by the difference in type and obtainment of characteristics, classification models and algorithms. Generally, the procedures involve two parts. The first one is carried out offline and aims at producing a classification model, that can either be constructed by experts, based on statistics, or obtained using machine learning techniques. The second part is the online application of the classifier for the detection of the process behaviour and possible faults. A visualization of this methodology is presented in Figure 1. The main requirement of data based PFD is that data is available and accompanied by diagnostic information. While in many cases historical data from operations is the main source, it is also possible to generate data and diagnostic information using an uncertain mathematical model. An example of this case is presented in this paper, that is concerned with data based PFD of an aerobic SBR WWT process treating 4-chlorophenol (4-CP, an inhibitory organic toxic compound) contaminated waste water. Given the absence of sufficient historical data, a process model that has been selected and identified from laboratory experiments and reported in the EOLI project 13 is introduced and transformed so that a continuous online estimate of the respiration rate during the SBR reaction phase with feeding can be obtained. This process signal has been widely recognized as an indicator for biological activity and employed for monitoring and control purposes 14.

Figure 1. Data based PFD methodology.

The usefulness of the respiration signal for the detection of a set of defined abnormal conditions (e.g. process faults) is verified through sensitivity analysis 15. Results from this analysis not only show the effects of parameter deviations but also indicate the characteristics that should be extracted from the respiration signal for a successful classification. Consequently, a feature extraction and classification procedure is proposed, which is designed to diagnose the formerly defined process faults. The paper concludes with results for diagnosis under conditions affected by uncertainties that are very common in bioprocesses and usually do prevent the straightforward application of well studied analytical PFD approaches.

2 Model

2.1 Process model

The studied process consists of five phases in the sequence that is given below and visualized in Figure 2:

1. Idle: The reactor is not in use.

2. Re-aerate: The biomass in the reactor is re-aerated to saturation, to ensure that oxygen is available when the substrate enters the reactor.

3. Fill and React: The working volume of the reactor is filled with residual water (influent) and microorganisms in suspension (activated sludge) within the reactor degrade organic and nitrogen compounds through metabolic activity.

4. Settle: The activated sludge sediments to the bottom of the tank.

5. Draw: The working volume of treated water is removed from the reactor (effluent).

Figure 2. Sequential process schema.

The process is operated with fixed time intervals as described in 16.

2.2 Reaction phase model

The EOLI project provided a validated model named EM1 17, which is based on concentrations and describes the dynamics of a 4-CP contaminated water treatment process through the following set of equations:

where X, S _C , S _O , μ, q _in , V, k ₁, k ₂, b, S _C,in , S _O,in , K _l a and S _O,sat represent the concentrations of biomass, organic matter and dissolved oxygen, the specific growth rate, the inlet flow rate, the volume, the yield coefficients, the endogenous respiration kinetic constant, the inlet organic matter and dissolved oxygen concentrations, the transfer coefficient and the oxygen saturation concentration, respectively.

The specific growth rate for the modelled single aerobic growth reaction is represented by the following Andrews model 18

where are the specific growth rate, the half saturation coefficient and the inhibition coefficient respectively. However, when the volume is not assumed constant, the nonlinear dynamics of the dilution term q _in /V presents difficulties which prevent a straightforward application of a linear solution. Nonetheless, the complete model can be transformed into a mass balance model using the facts that Concentration = Mass/Volume and that a measurement is available that allows to derive the actual volume in the reactor tank V

where m _x , m _s , m _o , V, μ _m , k ₁, q _in , c _s,in , k ₂, b, c _o,in , K _l a, m _o,sat are the biomass, the substrate mass, the dissolved oxygen mass, the liquid phase volume, the mass growth rate, the substrate to biomass conversion coefficient, the inflow rate, the concentration of substrate in the inflow, the oxygen to biomass conversion coefficient, the endogenous respiration coefficient, the dissolved oxygen concentration in the inflow, the oxygen mass transfer parameter and the dissolved oxygen mass at saturation, respectively. The mass growth rate is described by a volume dependent form of Equation 2.

where μ₀, K _s , K _i are the mass transformed specific growth rate, the half saturation coefficient and the inhibition coefficient, respectively, calculated from the parameters and coefficients from original model 16, assuming that V is available at any time through a measurement.

2.3 Respiration rate

In the case of aerobic WWT processes, the oxygen consumption rate of the biomass, called respiration rate in the following, has been widely recognized as an indicator for biological activity and employed for monitoring and control purposes 14. This has been verified in the studied case, where process dynamics obtained through changes in some parameters and initial conditions, are directly reflected in the respiration signal of the reaction phase, as presented in Figure 3.

Figure 3. Respiration profiles (nominal dashed, a with c _s,in  − 30% and m _x (0) + 30%, b with c _s,in  − 30%, m _x (0) + 30%, K _s  − 30% and K _i  + 50%, c with c _s,in  + 30%, m _x (0) − 30%; all deviations from nominal values).

Although respirometric equipment is commercially available, it represents an additional cost and maintenance factor and does not provide a continuous online estimation of the in situ respiration. An alternative possibility is to use a software sensor based on the oxygen balance and a dissolved oxygen concentration measurement to estimate the respiration rate r _m by software. The oxygen mass balance that is part of the process model ( Equation 3), actually includes the term that accounts for the respiration rate defined by Equation (6).

While it is possible to obtain r _m directly from the oxygen balance Equation (5) and the dissolved oxygen concentration measurement, it will be directly affected by any noise in the measurement. Thus, it is suggested to use a closed loop digital filter or observer to improve the estimation of r _m .

For continuous WWT processes, this has been suggested before by 19 and 20. For batch processes, 21 describe a method for obtaining respiration rates from a batch reactor in situ, but non-continuous. All of these methods assume a constant volume, an assumption that does not hold for the SBR operation considered here, where a change in volume will occur concurrently with the reaction. A discrete time observer that estimates the mass respiration rate r _m can be derived for Equations (5) and (6) similar to the one described in 22:

where

The estimate of the observer for depends on various factors, which have to be considered in a practical application. In particular, 22 discusses how to take into account the delay in the sensor response and how to calculate m _o,sat, without conflict for the observer (7).

3 Feasibility analysis of respiration rate based fault diagnosis

3.1 Sensitivity analysis of the respiration rate

The dynamics of the respiration rate are influenced by

	the initial condition of the biomass m x (0), which may change due to population dynamics or purging;
	the substrate concentration in the inflow c s,in , which may change due to waste water origin and productive process cycles;
	the extrinsic growth behaviour of the biomass on inhibitory substrates, that is given in Equation (4);
	K s is the half saturation coefficient;
	K i is the inhibition coefficient;
	μ0 is the specific growth rate;

which may vary due to a change in the population of microorganisms.

The analysis was therefore concentrated on these parameters, and it is assumed that the parameters are constant during the reaction phase. As an example, the time dependent sensitivity function of the variable r _m with respect to the initial condition m _x (0) is

where m _x (0) is the initial biomass and m _x (0)₀ is the nominal value of the initial biomass. This sensitivity function can be normalized with respect to the respiration rate signal as

The normalized sensitivity functions of m _x (0), c _s,in , K _s , K _i , μ₀ and K _l a during the reaction phase are presented in Figure 4. From the comparison of the graphs presented in this figure, the following observations can be made.

1. Deviations in c _s,in and m _x (0) affect the behaviour of r _m similarly, but the effect is distinguishable from the ones caused by deviations in K _s , K _i and μ₀.

2. The deviation of K _l a affects r _m during the complete phase and specifically in the minima, the second maxima and the end of the reaction phase.

3. The deviation of K _s affects r _m at the very beginning and at the second maximum.

4. The deviation of K _i strongly affects the second maximum of the signal.

5. The effect of deviations in K _s and K _i at the second maximum of the signal are opposed.

6. Deviations in μ₀ and K _i affect the behaviour of r _m similarly.

Figure 4. Normalized sensitivity functions (solid lines) of the parameters and initial conditions of interest and r _m (dashed lines).

3.2 Definition of faults

The parameters m _x (0) and c _s,in are commonly known to be within a certain range represented by the interval obtained from nominal value ± Δ%, where Δ is governed by SBR operating conditions. These parameters are therefore considered to be uncertain but not as faults and based on the first observation they can be distinguished from deviations in K _s , K _i and μ₀. On the other hand, deviations greater than nominal parameter value ± Δ% of the latter parameters are defined as abnormal conditions (faults) here. Considering the first observation, it was assumed that uncertainties in m _x (0) and c _s,in may occur concurrently, contrary to unpermitted deviations in K _s , K _i and μ₀ which, considering the last two observations, may be difficult to detect if faults occur at the same time. Slow changes in these parameters between reaction phases will lead to a detection in subsequent process cycles. The effect of the deviation in the K _l a on r _m ( Figure 4) indicates that large uncertainties in the transfer parameter may have a negative effect on the diagnosticability.

3.3 Estimation of the transfer coefficient K_la

Assuming that (a) the parameter K _l a changes only slowly when the air flow rate is constant 19 and (b) that respiration behaviour is invariable, the re-aeration phase ( Figure 2) can be exploited for its online identification and use the obtained estimate in the subsequent batch cycle for the estimation of r _m . Based on these assumptions, a discrete model can be obtained from Equation (5) using a zero-order-hold (ZOH) and reduced to

which represents the difference between two subsequent samples (i.e. at time k and k − 1) and describes the behaviour of the DO curve in an incremental form 23, p. 181], where ΔS _O (k − i) = S _O (k − i) − S _O (k − (i + 1)) and . Note that Equation (10) no longer depends on the S _O,sat and the respiration rate.

Using Equation (10), two identification algorithms for the parameter K _l a have been implemented. Both can be applied if re-aeration starts from an initial condition value S _O (0) << S _O,sat − r _e and ends near steady state conditions ( , or S _O ≅ S _O,sat − r _e ).

1. A linear regression (least squares estimate), using all samples obtained during the re-aeration period, a standard offline parameter identification method as described in 24, Sec. 4.1.

2. A Kalman filter for parameter identification, an online parameter identification method as described in 24, p. 325.

The advantage of the Kalman algorithm over a recursive least squares algorithm is the fact that literature suggests values for the initial values of the parameter and the filter parameters. Both implementations have been successfully verified in simulation and with data from EOLI model identification experiments. Figure 5 presents an example for identification using online measurement data. is the result of the Kalman filter algorithm when started from the point in time when aeration is switched on (with initial covariance P(0) = 100 and θ(0) = 0), is the result when the algorithm starts after one can assume that the aeration system has achieved steady state. The latter is slightly better, as the starting point and the first part of the re-aeration curve is the most critical part for the identification and is influenced by the delay of the aeration mechanism in aerating the reactor. These results are comparable to reported by 13 for the same data.

Figure 5. S _O for parameter identification in the re-aeration phase.

The implementation of the online identification of the oxygen transfer parameter K _l a over consecutive cycles allows to enhance the result using the estimated as initial value θ(0) for the algorithm in the subsequent cycle.

4 Fault diagnosis

4.1 Selection of characteristics of the respiration rate

Based on the observations and the faults defined in Section 3.1, the following selection of characteristics is proposed to be extracted from the respiration signal are as follows:

	t max,1, the time until the first maximum r max,1
	r max,1, and r max,2 the two maxima
	r min, the minimum between the two maxima
	The geometric properties of the triangle a t , b t , c t , α t , β t and γ t , that are defined by the points r max,1, r max,2 and r min.

Additionally, there are two other characteristics that can be extracted from the respiration rate signal, which have been selected based on experience of human experts:

	r e , the endogenous respiration estimate and
	r tot , the total metabolic respiration defined by

The complete set of characteristics is

Except t _max,1 they are indicated in Figure 6.

Figure 6. Characteristics of the nominal respiration rate signal.

For standardized results, the characteristics are obtained and calculated from a min–max normalization of the signal, by locating the minima and maxima specific for the studied case. Signals that are qualitatively different from the nominal pattern in Figure 3 can be detected at this point but not diagnosed. However, they have diagnostic interpretations known to the human expert: (i) in Figure 3, a and b mean little or no inhibition and (ii) c means reaction unfinished.

4.2 Process data with diagnostic information

The basis for the FDI schema presented in Figure 1 is historical process data with corresponding diagnostic information. However, in the investigated SBR process case, only few experiments were available, mainly due to the fact that these experiments are very time- and cost-intensive. Nonetheless, the analytical process model Equations (3) and (4) provides the possibility of generating the required data. The expected uncertainties in parameters and initial conditions can be taken into account with simulations that use a random sampling approach.

4.3 Classification

The detection of an unpermitted deviation in one of the parameters K _s , K _i or μ₀ will be represented by a set of two classes and for the isolation, two more sets of 4- and 7 classes providing additional information about the fault will be considered:

1. 2-classes: {normal, abnormal} representing detection only;

2. 4-classes: {K _i , K _s , μ₀, normal} representing detection of unpermitted deviation and isolation of the parameter that changed; and

3. 7-classes: {K _i,low, K _i,high, K _s,low, K _s,high, μ_0,low, μ_0,high, normal} representing detection of the unpermitted deviation, isolation of the parameter that changed and the direction of the change;

where normal stands for normal behaviour, abnormal for a change in one of the parameters, K _s , K _i and μ₀ for a change in the corresponding parameter and K _s,low, K _s,high, K _i,low, K _i,high, μ_0,low and μ_0,high for a change in the respective parameter and the direction of change.

The classification models themselves can be categorized in two groups:

1. Black-box models: The acquired knowledge is implicit (e.g. ANN).

2. White-box models: The acquired knowledge is explicit (e.g. rules or decision trees).

Since in some applications it might be of interest to have access to the knowledge extracted from the process data in explicit form, one algorithm of each category has been chosen to allow a comparison and a choice for the application in other aerobic batch wastewater treatment processes. The selected implementations of the algorithms are part of the WEKA Machine Learning Toolkit 25. (i) J48 is an implementation of the C4.5 algorithm for machine learning of decision trees. This algorithm requires very few time for learning and yields a white-box model. (ii) MLP is an algorithm that constructs a simple multilayer perceptron and trains it by means of back-propagation. The number of input nodes, output nodes and of nodes in the single hidden layer is equal to the number of characteristics in the set ( Equation 12), the number of diagnostic classes and a fixed ratio between the first two, respectively. This algorithm requires an order of magnitude more time for learning and yields a black-box model.

5 Results

The method proposed for fault diagnosis based on the uncertain mathematical model has been verified with a set of simulations. These take into account uncertainties of ±25% in m _x (0), the initial biomass and c _s,in the substrate concentration in the inflow, as well as an error of 5–10% in the identification of the parameters K _s , K _i and μ₀. The inflow rate q _in as well as all other parameters have been assumed to be known and constant.

To obtain classification results for feature sets that have not been used for training, the complete generated data set has been randomly permuted and split into training (2/3) and test (1/3) sets. The first has been used as input for the machine learning algorithms that yield the classification models for the detection (2-classes) and diagnostic cases (4-,7-classes). The latter has been used to obtain the classification results for unknown feature sets that have not been used for training. A 10-fold cross validation ensures that the results are representative for an online use of the generated classification models. A comparison of the average of the classification results of the 10 folds of the two types of classifiers and the three sets of diagnostic classes is presented in Figure 7.

Figure 7. Comparison of classification results.

6 Conclusions

A signal-based PFD procedure is presented, that is based on the selection of characteristics and classification algorithms with an uncertain mathematical model. The employed model describes the corresponding aerobic SBR process that treats waste water contaminated with 4-chlorophenol, an inhibitory organic toxic compound. In a first step, the original concentration based model is transformed to a mass balance model that allows to estimate the respiration rate during the fill and reaction phase of the process.

Changes in the behaviour of the respiration rate signal due to variations in parameters are evaluated through the application of sensitivity analysis. The results from the analysis (i) confirm that the respiration rate is indeed a good indicator for biological activity that can be used for PFD; (ii) show that it is possible to discern between nominal and faulty behaviour in spite of specific uncertainties, if the oxygen transfer parameter K _l a is estimated periodically; and (iii) indicate the signal characteristics that should be extracted from the signal for a successful classification for PFD.

Consequently, an estimation method for the transfer parameter K _l a and an extraction procedure for the signal characteristics is presented. The latter are employed to construct classification models through well-known machine learning algorithms for pattern recognition.

Results show that despite the above mentioned uncertainties proposed, the PFD procedure is quite successful, given that the percentage of correct diagnosis is above 95% in almost all cases. This indicates that the machine learned classification models can be used online for the detection and diagnosis of certain process faults, which cannot be detected by a straightforward application of analytical PFD approaches.

Acknowledgements

This paper includes the results of the EOLI project that is supported by the INCO program of the European Community (contract number ICA4-CT-2002-10012).