Unified model-based fault diagnosis for three industrial application studies

Control Engineering Practice 19 (2011) 479–490

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Control Engineering Practice journal homepage: www.elsevier.com/locate/conengprac

Unified model-based fault diagnosis for three industrial application studies ¨ Udo Schubert a,b, Uwe Kruger b,, Harvey Arellano-Garcia a, Thiago de Sa´ Feital b,c, Gunter Wozny a a b c

Chair of Process Dynamics and Operation, Berlin Institute of Technology, Str. d. 17. Juni 135, 10623 Berlin, Germany Department of Chemical Engineering, The Petroleum Institute, P.O. Box 2533, Abu Dhabi, United Arab Emirates Programma de Engenharia Quı´mica/COPPE, Universidade Federal do Rio de Janeiro, 68501 Rio de Janeiro, Brazil

a r t i c l e i n f o

abstract

Article history: Received 23 November 2009 Accepted 31 January 2011

This paper proposes a unified scheme for fault detection and isolation (FDI) that integrates model-based and multivariate statistical methods. For creating suitable models, subspace model identification is utilized together with state-observers to track the measured process operation. To describe and analyze the impact of fault conditions, the scheme utilizes input reconstruction and unknown input estimation to generate multivariate residual-based statistics. In contrast to existing work, the paper presents three industrial application studies involving sensor faults, as well as process and actuator faults which result from measured and unmeasured disturbances. & 2011 Elsevier Ltd. All rights reserved.

Keywords: Unknown input observer Input reconstruction Fault detection Fault isolation

1. Introduction The ever increasing complexity of systems in the manufacturing and chemical industries has rendered efficient process monitoring by human operators to become a difficult task. This stems from increasing levels of process optimization and intensification, which gives rise to operating conditions that are at the limits of operational constraints and which yield complex dynamic behavior (Schmidt-Traub & Go´rak, 2006). A consequence of these trends is a reduced safety margin if the process shows some degree of abnormality, for example caused by a fault (Schuler, 2006). Suitable and efficient monitoring methods are therefore required (i) to allow a comprehensive monitoring of the dynamic operation by plant personnel, (ii) to offer the ability to detect fault conditions and (iii) to provide suitable information to support the diagnosis of the underlying root cause. Over the past decades, the research community achieved significant progress in the area of process monitoring by developing approaches that utilize causal models, referred to as modelbased fault detection and identification (MBFDI), as well as multivariate statistical process control (MSPC). The benefit of utilizing causal models over MSPC methods lies in their accuracy of describing the underlying process dynamics (Ding, 2008). However, the cost and effort in developing models increases substantially with the complexity of the process. In contrast, MSPC methods are designed for applications to large-scale processes

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E-mail address: [email protected] (U. Kruger). 0967-0661/$ - see front matter & 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.conengprac.2011.01.009

since they only require historical process data, as discussed in Yoon and MacGregor (2001) for example. The literature has proposed various schemes for MBFDI (Ding, 2008; Frank, Ding, & Marcu, 2000; Isermann, 2006; Simani, Patton, & Fantuzzi, 2002; Venkatasubramanian, Rengaswamy, Yin, & Kavuri, 2003). Application studies for detecting abnormal moisture levels and an FDI benchmark study involving an industrial actuator are reported in Odgaard and Mataji (2008) and Puig et al. (2006), respectively. To increase the robustness of observerbased state estimations, unknown input observers (UIOs) have been introduced to achieve a decoupling from unknown disturbances (Simani et al., 2002). Related to UIOs, another research stream is the development and application of input estimators. These have shown their potential in the monitoring of dynamic processes through numerous application studies (Chang, You, & Hsu, 1997; Gao & Ding, 2007b; Muller, 2000; Xiong & Saif, 2003). Although a theoretical framework of UIOs and input reconstruction schemes is laid out (Hui & Zak, 2005), applications have predominantly focused on numerical examples of linear systems (Xiong & Saif, 2000), linear or nonlinear models of simulated plants (Sotomayor & Odloak, 2005) and few applications on recorded data of small-scale systems (Edwards, 2004). Addressing the difficulties in obtaining a causal model for large-scale systems several contributions suggested the combination of MBFDI and MSPC (Ding, 2008; Venkatasubramanian, Rengaswamy, Kavuri, & Yin, 2003; Yoon & MacGregor, 2000). For MSPC-based fault diagnosis Gertler and Cao (2004) and Yoon and MacGregor (2001) studied the incorporation of the fault isolation capability of MBFDI. The general lack of accurately describing dynamic process behavior using MSPC remains with

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this approach, which has the potential to lead to incorrect and misleading results. Ding, Zhang, Naik, Ding, and Huang (2009) and Sotomayor and Odloak (2005) examined the incorporation of subspace model identification (SMI) into MBFDI to handle the modeling task for large-scale systems. This presents a framework for monitoring the typically large number of highly correlated variables (Qin, 2003) using MBFDI methods. Ding et al. (2009) suggested the design of a residual generator in the parity space, where standard MBFDI methods are not applicable. Sotomayor and Odloak (2005) utilized a state space model for MBFDI but only addressed simple sensor and actuator faults. It should also be noted that the statistical evaluation of residuals generated by the MBFDI scheme is based on simple univariate hypothesis testing for changes in the mean or variance, the presence of a step change or the analysis of auto-correlation (Ding, 2008; Isermann, 2006). A multivariate analysis of such residuals has therefore not been considered in the literature. Given that an identified SMI model is accompanied by model uncertainties and unmodeled dynamics, the residuals may be correlated which is a scenario for which MSPC methods have been developed. Irrespective of the reported success of combining MBFDI and MSPC, a unified approach with the aim of detecting and diagnosing sensor, actuator and process faults has not yet been proposed in the research literature. This is the main contribution of this paper along with the presentation of application studies to industrial process units for which various sensor and process faults were recorded.

2. Preliminaries This section gives a brief overview of relevant MBFDI and MSPC tools to develop the proposed FDI scheme in Section 3 and cites the key references from the literature that may be consulted for further information. The relevant material of MBFDI using input reconstruction and estimation is described first. This is followed by a summary of SMI algorithms and the description of univariate monitoring statistics commonly employed in MSPC applications. 2.1. Model-based FDI A linear time-invariant causal model in state space form has the following description: xðkþ 1Þ ¼ AxðkÞ þ BuðkÞ þ EwðkÞ,

ð1Þ

yðkÞ ¼ CxðkÞ þ DuðkÞ þFvðkÞ, n

ð2Þ l

where xðkÞ A R is the state vector, yðkÞ A R is the output vector, uðkÞ A Rm is the input vector, vðkÞ A Rr describes output uncertainties (e.g. measurement noise or sensor faults), and wðkÞ A Rs represents uncertainty of states (e.g. due to common cause process noise, or process and actuator faults) for the kth sample. Model-based FDI approaches use Eq. (1) together with state ^ observers to create an estimate xðkÞ of the state variables and evaluate the prediction error of the measured outputs ^ eðkÞ ¼ yðkÞyðkÞ. Any significant increase in this error is indicative of anomalous behavior. To increase the robustness of the state estimation, the literature advocates the use of UIOs in case of unmeasured disturbances with known distributions described in E (Hui & Zak, 2005). For FDI applications, input reconstruction or the estimation of system inputs has also been discussed to detect sensor and actuator faults

(Edwards, 2004; Fang, Shi, & Yi, 2008; Gao & Ding, 2007a; Muller, 2000; Tan & Edwards, 2003; Xiong & Saif, 2003). 2.1.1. Unknown input estimation UIOs decouple state estimates from unmeasured disturbances (Hui & Zak, 2005). Eq. (1) can therefore be augmented by additional inputs that represent sensor fault conditions (Edwards, 2004), while the unknown process noise contribution is neglected: vðk þ1Þ ¼ Av vðkÞ þ nðkÞ:

ð3Þ

The faults are thereby considered to be the response of a dynamic system Av to the unknown additive sensor fault nðkÞ A Rr with r r l. During normal operation, the fault vector nðkÞ can be considered to follow a zero mean Gaussian distribution. Augmenting the state vector by the fault vector n, the original system (1) becomes # !   ! "   xðkÞ xðkþ 1Þ A 0 B 0 ¼ þ uðkÞ þ nðkÞ, ð4Þ vðkÞ vðk þ1Þ 0 Av 0 I |ffl{zffl} |fflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflffl} |fflfflfflfflfflfflffl{zfflfflfflfflfflfflffl} |fflfflfflfflffl{zfflfflfflfflffl} |ffl{zffl} Aa

xa ðk þ 1Þ

xa ðkÞ

Ba

Ea

where the subscript a refers to the augmented form of Eq. (1). To describe the impact of additive sensor faults nðkÞ upon the outputs, F is set to the identity matrix since each sensor fault only affects a single output variable: ! xðkÞ yðkÞ ¼ CxðkÞ þ DuðkÞ þ FvðkÞ ¼ ½C I þ DuðkÞ ¼ Ca xa ðkÞ þ DuðkÞ: vðkÞ ð5Þ Consequently, a prediction error that results from a sensor fault will be compensated through the observer by non-zero elements for vðkÞ in the augmented state vector xa. Therefore, the estimates x^ a are robust against sensor faults, acting as unknown inputs to the system to Eq. (4) and an estimate of the sensor fault signature for a given Av ^ is included with vðkÞ. To achieve the desired decoupling property, recent suitable design approaches for full and reduced order UIOs can be found in Hui and Zak (2005) and Simani et al. (2002). 2.1.2. Input reconstruction Apart from process noise, the vector w(k) in Eq. (1) can also represent modeling errors, input uncertainty or process faults (Edwards, 2004; Yoon & MacGregor, 2000). This can be addressed by reconstructing the noise vector that corresponds to the fault condition using state estimates (Edwards, 2004; Sotomayor & Odloak, 2005): ^ ^ þ1ÞAxðkÞBuðkÞÞ ^ ^ þ 1Þxðk ^ þ1jkÞÞ, wðkÞ ¼ Ey ðxðk ¼ Ey ðxðk y

T

ð6Þ

1 T

where E ¼ ½E E E is the generalized inverse of E, which is estimated for normal process operation, or designed for specific ^ þ 1jkÞ is the model prediction of the state fault scenarios, and xðk ^ vector for sample k þ 1 using the state estimate xðkÞ and control ^ input u(k) from the previous step. According to Eq. (6), wðkÞ is assumed to be described by a zero mean multivariate Gaussian distribution under normal operating conditions. Any significant ^ change in the first or second order statistics of wðkÞ is therefore indicative of the presence of an actuator or process fault. 2.2. Subspace model identification Using first-principle models of complex industrial processes is usually not feasible for MBFDI approaches (Venkatasubramanian, Rengaswamy, Yin, et al., 2003). However, as reported in Van Overschee and De Moor (1996), practical experience has shown that industrial processes can be approximated with sufficient accuracy by linear time-invariant systems of finite dimensions. Using recorded input/output process data, SMI methods allow an estimation of the system order produce estimates of the

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system matrices A, B, C and D and extract statistical parameters describing the characteristics of the process and sensor noise. Based on Eq. (1) future samples of the output variables can be described by Yf ¼ CXf þ HUTf þEf , where C is the extended observability matrix, H is the lower triangular Toeplitz matrix and Ef describes the impact of the sensor and process noise. The matrix product CXf can be predicted from past data samples stored in ½Yp Up  (Van Overschee & De Moor, 1996). The literature has proposed different SMI algorithms that either ^ use estimates of the state sequence xðkÞ or an estimate of C to extract the state space matrices (Favoreel, De Moor, & Van Overschee, 2000; Shi & MacGregor, 2000; Van Overschee & De Moor, 1996). It should be noted that the model accuracy is a crucial factor for the performance of any FDI scheme in order to prevent false alarms and an incorrect diagnosis. To guarantee a sufficiently accurate model, the recorded data set for identifying an SMI model stems, in the ideal case, from designed experiments that guarantee an adequate level of excitation in all input channels. For the application studies summarized in this article, the free subspace identification toolbox from van Overschee (2002) was used, which is based on weighted CVA to achieve a maximum impact of correlation among input and output variables on the generated system matrices. 2.3. Univariate monitoring statistics Based on the generated residuals, univariate statistics can be constructed to discriminate normal from abnormal behavior. The ^ estimates of the output variables form the prediction error eðkÞ ¼ ^ yðkÞyðkÞ, that allows the construction of a residual squared prediction error (SPE) statistic, which is defined as SPE(k)¼ eT(k)e(k). Following the discussion in Nomikos and MacGregor (1995), the distribution function of the SPE statistic can be approximated by a w2 distribution to calculate a control limit SPEa for a given significance a. ^ In contrast, the generated input reconstructions wðkÞ allow the construction of Hotelling’s T2, which is defined as T 2 ðkÞ ¼ 1 ^ T ðkÞS^ ww wðkÞ, ^ w With S^ ww being the estimated covariance matrix of w. Since T2 statistic follows an F-distribution (Tracey, Young, & Mason, 1992), appropriate control limits can also be obtained for a significance a, e.g. 1% or 5%.

3. Unified MBFDI/MSPC scheme This section develops the proposed FDI scheme, which is designed to detect simple sensor and actuator faults as well as complex process faults and offers a generic fault diagnosis capability. The methods discussed in the previous section are utilized in a unified manner to overcome some of the limitations of MBFDI and MSPC approaches possess when applied individually. The first subsection introduces the general framework. Sections 3.2 and 3.3 then show how to apply this scheme for detecting and diagnosing sensor, actuator and process faults. Finally the required steps for diagnosing simultaneously occurring fault conditions are highlighted in Section 3.4. 3.1. Introduction of the unified approach The relation between the domains MBFDI and MSPC, and the proposed unified MBFDI/MSPC scheme is summarized in Fig. 1. The upper part of this figure shows the individual approaches that provide the techniques utilized in the unified approach. The lower area of the figure describes the unified MBFDI/MSPC method. The

481

MBFDI

MSPC

Input Observer Estimation/ Reconstruction Parameter Enhanced Estimation Residuals Kalman Filter

Parity Equations

SMI

Fault Detection Indices

DPCA PLS CVA

Contribution Plots PCA

Model Identification Subspace Model Identification Residual Generation Input Estimation/ Reconstruction Fault Detection Multivariate Fault Detection Indices Fault Diagnosis Enhanced Residuals Unified MBFDI/MSPC Scheme Fig. 1. Unified approach using a combination of MSPC and MBFDI methods for tasks in FDI.

core of the proposed FDI scheme is the model-based approach, where the dynamic model is identified using SMI, which is a method that has recently been employed in conjunction with MSPC approaches (Lieftucht et al., 2009; Xie et al., 2006). The issue of requiring first-principle models for the FDI task is therefore overcome by invoking an identified state space model, since practical experience has shown that industrial processes can be approximated with sufficient accuracy by such models (Van Overschee & De Moor, 1996). This, however, implies that the model can only be employed for operating regions where reference data are available, or where the model accuracy can be evaluated using process data that stem from a designed excitation of the process. The following two subsections describe in detail how the tasks of fault diagnosis are tackled.

3.1.1. Fault detection The identified state space models are embedded in the generation of observer-based residuals (MBFDI). The recorded input/ output variables are utilized to track current process behavior through estimated state sequences. The generated residuals are then analyzed by the univariate T2 and SPE statistics, discussed in Section 2.3. The utilization of these MSPC statistics for an MBFDI scheme has not yet been discussed in the literature. The benefit of constructing nonnegative quadratic forms from the residuals is a robust fault detection, as structured residuals are known to be sensitive for model uncertainty (Isermann, 2006) and lead to false alarms due to induced correlation. Consequently, incorporating covariance information of the residuals from periods with common cause process variations by defining the T2 and SPE statistics yields a robust fault detection.

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3.1.2. Fault diagnosis Fault diagnosis is the most challenging task for MBFDI and MSPC. Traditionally, MSPC relies on contribution plots (Kourti & MacGregor, 1996) or variable reconstruction (Alcala & Qin, 2009; Lieftucht et al., 2009). To diagnose simple sensor or actuator faults, e.g. a bias or a drift, these methods have shown to work well. If the abnormal condition is described by a complex fault, however, these MSPC methods have the potential to show ambiguous or even misleading results (Alcala & Qin, 2009; Lieftucht et al., 2006). This stems from complex interactions between the recorded process variables which can yield that a faulty variable affects several other variables at the same time (Yoon & MacGregor, 2001). Examples are parametric faults or unmeasured input disturbances. In such circumstances a contribution plot will correctly identify a large number of contributing variables, but this seriously hampers the fault diagnosis task. For MBFDI, disturbances or incipient faults can be expressed by unknown inputs (Xiong & Saif, 2003). Compared to MSPC diagnosis methods, this allows a direct estimation and visualization of the propagation of the fault. Examples of such fault propagation are given in Section 4. The proposed unified MBFDI/ MSPC scheme uses a generic reconstruction of inputs to provide a causal explanation for the error between measured and predicted output variables through the calculation of input variables. In fact, we invert the model to determine input residuals that can describe the fault propagation of a complex process fault by contrasting the observed plant behavior with that of the identified process model. It should be noted that the proposed fault diagnosis approach is data driven and does not require a priori knowledge through past data describing the detected fault. Moreover, the computed fault signatures furnish an experienced plant operator with a visual aid to narrow down potential root causes of this process abnormality. It should also be noted that the research community has not yet discussed the utilization of computed input residuals through model inversion. Section 3.3 gives mathematical details for computing the input residuals.

3.2. FDI for sensor faults The literature has comprehensively studied and analyzed various schemes for sensor fault diagnosis (Isermann, 2006; Simani et al., 2002). These schemes either rely on enhanced residuals or a bank of observers for fault diagnosis. Using the disturbance decoupling property of UIOs, the robustness of observer-based FDI can be enhanced if information about the dynamic propagation of a disturbance exists. Following the discussion in Section 2.1.1, a bank of UIOs, embedded in a generalized observer’s scheme (Simani et al., 2002) is constructed by augmenting the state vector for every potentially failing sensor. More precisely, if l¼5 there are a total of five UIOs (one for each sensor). Using the unified MBFDI/MSPC scheme, the SPE statistic, detailed in Section 2.3, is monitored to determine if any of the sensors are faulty. Upon detection, isolating which sensor is faulty and to extract the magnitude and signature of the sensor fault relies on the augmented UIOs. This diagnosis task is based on a two-step procedure. To isolate which of the sensors is faulty, the SPE statistic for each of the l augmented observers is analyzed. Assuming that the ith sensor is faulty, only the augmented state vector that represents the ith output variable will generate an SPE statistic that does not violate the statistical control limit. More precisely, given that the ith observer includes this sensor fault as an additional state, it is able to minimize the estimation error, even though it relies on faulty measurements. The remaining observer include different sensor faults, which, in turn, cannot

compensate the faulty measurement. Subsequently, with the faulty sensor being isolated, the estimate of the additional state variable v^ i for the ith augmented observer describes the magnitude or signature of the sensor fault. Section 4.1 presents an example of detecting and diagnosing a sensor fault for an industrial furnace process. 3.3. FDI for actuator and process faults In contrast to simple sensor faults, process faults cannot be attributed to individual sensors and actuator faults have a multiplicative effect on the output variables. Hence, the diagnosis scheme discussed in the previous subsection is not applicable here and a more complex mechanism for diagnosing such faults is required. Despite the fact that a conventional observer estimates state sequences to minimize e(k), the underlying state space model does not describe the effect of the fault condition. More precisely, the state to output relationship may not yield the fault condition by examining the output residuals. The input to state relationship, however, must therefore describe the plant model mismatch in the presence of a fault. This gives rise to revisit Eq. (6) to formulate input residuals: ^ ^ þ 1ÞAxðkÞ: ^ uðkÞ ¼ By ½xðk

ð7Þ

Here, By is the generalized inverse if n Zm. The case where m 4 n, which is not a frequent occurrence in practice, will be elaborated ^ ^ upon later in this subsection. Defining uðkÞ ¼ uðkÞ þ DuðkÞ, where u(k) is the measured input vector for the kth sample, Eq. (7) can be rewritten as follows: ^ ^ þ 1ÞAxðkÞBuðkÞ ^ ¼ By ½xðk DuðkÞ

ð8Þ

or alternatively ^ ^ þ 1Þxðk ^ þ 1jkÞ DuðkÞ ¼ By ½xðk

ð9Þ

^ ^ þ BuðkÞ. It is important to note that by using xðkþ 1jkÞ ¼ AxðkÞ Eq. (9) is non-zero if and only if the deterministic prediction of the ^ þ1jkÞ using the model is different from the state vector xðk ^ þ1Þ using the observer. An interpretation of estimated state xðk ^ Eq. (8) is that the input residuals DuðkÞ describe the required input action that is necessary to compensate for the fault condition. Following this interpretation, the generated input residuals may include information about actuator or process faults at the same time. This will be discussed later in this section. The preceding discussion outlines that the SPE statistic may not be suitable for a robust detection of an actuator or a process fault. However, a univariate T2 statistic that is based on the input ^ residuals DuðkÞ is sensitive to such faults. With Efg being the ^ ¼ 0 holds in the fault-free case. This expectation operator EfDuðkÞg follows from E{w(k)} ¼0 and E{v(k)}¼ 0 for the causal model in Eq. (1). For the identified state space model, the same assumptions can be imposed upon the model residuals (Van Overschee & De Moor, 1996). Given that a reference set describing NOC can be used to determine the error covariance matrix S^ DuDu , Hotelling’s T2 becomes T

^ T 2 ðkÞ ¼ Du^ ðkÞS^ DuDu DuðkÞ:

ð10Þ

Under the assumption that S^ DuDu has been estimated independently from the state space model, T 2  Fðm,KmÞ (Tracey et al., 1992), where F(m,K  m) is an F-distribution with m and K  m degrees of freedom and K is the number of reference samples. For a sensitivity a, the NOC yields T 2 ðkÞ r Ta2 , whilst T 2 ðkÞ 4 Ta2 implies the presence of an actuator or process fault. Fault detection is followed by a subsequent fault diagnosis, which consists of a thorough analysis of the computed input residuals. As mentioned above, the input residuals yield the

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necessary input for compensating the fault condition. Therefore, they describe a quasi-causal interpretation that allows a diagnosis into the root cause of a detected fault. This can be an actuator fault for which only a single element of the residual vector becomes nonzero, for example a sticking valve or a wearing pump. On the other hand, a complex process fault, which results from an internal phenomenon within the process represents a characteristic pattern of nonzero residuals. Using a causal analysis, these residuals then indicate the potential root cause of an event. The presented application studies in Sections 4.2 and 4.3 demonstrate how the input residuals yield such patterns within ^ the sequences DuðkÞ and how to utilize these patterns for diagnosing complex process fault conditions. Cases where a pseudoinverse cannot be found for B A Rnm if ^ þ1Þxðkþ ^ ^ m 4n are now discussed. Abbreviating xðk 1jkÞ ¼ DxðkÞ, a T2 statistic can be constructed as follows: 1 T ^ T 2 ðkÞ ¼ Dx^ ðkÞS^ DxDx DxðkÞ:

ð11Þ

Whilst this allows fault detection a direct fault diagnosis cannot ^ A Rn and uðkÞ A Rm . Rewriting Eq. (8) be considered since DxðkÞ yields ^ ^ þ 1ÞAxðkÞBuðkÞ: ^ ¼ xðk BDuðkÞ

ð12Þ nn

Partitioning B into a squared matrix B1 A R B2 A RnðmnÞ gives rise to 1 ^ ^ Du^ 1 ðkÞ þB1 1 B2 Du 2 ¼ B1 DxðkÞ:

and a matrix ð13Þ

^ Given that DuðkÞ must contain linearly dependent elements, Eq. (13) allows an experienced process operator to narrow down potential root causes by applying a priori knowledge. For example, ^ ~ elements of DuðkÞ that are unlikely to correspond to a fault m condition can be set to zero. The contribution of the remaining inputs can then be computed as a quadratic programming ^ ~ 4 n or by problem to minimize the length of DuðkÞ if mm ^ ~ Du^ 1 ðkÞ ¼ B1 1 DxðkÞ if mm ¼ n.

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It should be noted that the description of faults through matrix E is not a trivial task, since process faults may have time-varying and nonlinear behavior. Additionally, the existence conditions of a UIO for the resulting system (14) may be rather restrictive, since they include a rank condition like rankðCEa Þ ¼ rankðEa Þ. The next section present application studies that involve the analysis of a sensor fault, a complex process fault and an actuator fault to demonstrate the utility of the proposed MBFDI/MSPC scheme.

4. Industrial applications This section presents a total of three case studies to show the wide range of FDI applications the proposed approach, detailed in the previous section, can cover. These industrial application studies were carefully selected to include examples of a sensor fault, a complex process fault and a fault condition that relates to an unknown actuator fault. Moreover, these application studies were based on recorded data from various industrial processes to underpin the practical importance of correctly detecting and isolating fault conditions. First, Section 4.1 summarizes an application study involving a sensor fault, describing a failing temperature sensor of an industrial furnace as well as the estimation of the true sensor reading. The second application study, discussed in Section 4.2, then describes a complex process fault that results from a measured disturbance and is characterized through changed process dynamics. This case highlights the benefit of utilizing dynamic models for residual generation and how the generated input residuals enhance the identification of the root cause of the fault. Finally, the case of an actuator fault is examined, which corresponds to an unmeasured disturbance and is presented in Section 4.3.

3.4. FDI for simultaneous faults

4.1. Sensor fault detection in a heating furnace

As process faults may develop over a time span ranging from a few hours to days or even weeks, sensor faults may arise rather instantly and sometimes recover after a short period of time. It is therefore desirable to have an FDI scheme that can handle the presence of simultaneous sensor, actuator and process faults. This poses a challenging task, since a deviation of output variables can now be the result of a developing process fault and the simultaneous presence of a sensor bias or a sensor drift. The solution lies in a robust state estimator that is capable of providing robust state estimates, even if both types of faults occur simultaneously. This gives rise to the design of a UIO according to Section 2.1.1, but without neglecting the process noise matrix E: ! " # ! !     xðk þ 1Þ xðkÞ wðkÞ A 0 B E 0 ¼ þ uðkÞ þ : nðkÞ vðk þ 1Þ vðkÞ 0 Av 0 0 I |ffl{zffl} |fflfflfflffl ffl {zfflfflfflffl ffl } |fflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflffl} |fflfflfflfflfflfflffl{zfflfflfflfflfflfflffl} |fflfflfflfflffl{zfflfflfflfflffl}

This application study involves an intermediate heating furnace, that is part of a powerforming process. This catalytic reforming process takes light naphtha to produce a high-octane liquid product in fixed-bed reactors, supported by a catalyst, at elevated temperatures and high hydrogen pressures. Furnaces play an important role in process plants, as they elevate the temperature of raw materials or intermediate products to high temperature levels required to enhance the performance of downstream reaction sections. The harsh environments inside a furnace can present challenges for robust sensor readings, which, however, are important for a robust closed loop control.

xa ðk þ 1Þ

Aa

xa ðkÞ

Ba

Ea

ð14Þ If the existence conditions of the chosen design approach (Hui & Zak, 2005; Simani et al., 2002) are met, the observer generates state estimates, that are robust against sensor faults with the dynamic properties described in Av and process or actuator faults with the corresponding distribution E. While the sensor fault signature is available as part of the augmented state vector xa as in Section 3.2, the propagation of process or actuator faults in w(k) can be reconstructed using Eq. (6). In this case, the same fault detection methods, described in Sections 3.2 and 3.3, are applicable.

4.1.1. Plant operation The furnace operates at different fuel gas pressure levels with an uncontrolled fuel gas flow depending on the current operating point. The upstream naphtha-feed from the first reactor consequently leaves the furnace with a varying temperature before entering the main furnace, where its temperature is elevated to the specification of the second reactor. Details about catalytic reforming processes can be found in Pujado´ and Moser (2006), whereas Fortuna, Graziani, and Barbalace (2005) summarized a case study to a process similar to that analyzed here. A preanalysis of the recorded data shows that normal operation presents considerable common-cause variations. Over a period of 14 days, a data set was recorded with a sampling period of 30 s. Table 1 shows the set of variables used in the presented analysis.

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4.1.2. Fault description It is known that thermocouples for measuring skin temperatures have measurement biases but usually recover after some hours. Advanced process control, however, relies on accurate sensor information, e.g. to compute optimal setpoints or process trajectories. A sensor bias could therefore have a pronounced effect on process performance. Hence, it is required to detect such faults and to reconstruct the exact fault magnitude and signature to prevent such events from propagating and consequently affecting product quality. Throughout the recording period, several occurrences of measurement biases were noticed. The following two sections summarize the analysis of one such instance. 4.1.3. Model development and fault detection To identify a state space model a subset covering around 50 h of data (6200 samples) was used. The application of SMI suggested the inclusion of n¼ 10 state variables and showed a good performance for predicting skin and naphtha outlet temperatures. Next, a bank of UIOs was designed. Each observer included one additional variable, leading to a bank of 10 different augmented UIOs. With respect to Eq. (4), the matrix Av reduces to a scalar and a value of 0.6 was selected for each augmented UIO, since each of the output variables represents temperature measurements that fall within a narrow range of about 20 1C. The selection of Av ¼ 0.6 is based on the discussion in Saif and Guan (1993), which advocates the design to be such that the stable system responds quickly to a step-type fault condition. Table 1 Process variables of the intermediate furnace.

Utilizing the SPE statistic, for which SPEa ¼ 103 was computed for the significance a ¼ 0:01, the detection of sensor fault could now be carried out. Fig. 2 summarizes the results of analyzing a fault for skin temperature 5, y5. The upper left plot in Fig. 2 shows that this sensor bias was detected less than 5 min after the initial slight departure from the correct reading arose. 4.1.4. Fault diagnosis Identifying which sensor is faulty relied on the use of individual SPEi statistics. Investigating the 10 different UIOs yielded that augmenting the state vector by the 5th output variable did not lead to significant violations of the control limit. The upper right plot in Fig. 2 shows the individual SPE statistics for the UIOs augmented by the 4th, 5th and 6th sensors and confirms that only the SPE5 statistic did not produce any significant violations. In contrast, utilizing the other nine UIOs led to constant violations between 436 and 536 min into the data set. After confirming which sensor produced a bias, the lower left plot in Fig. 2 depicts the predicted values for sensors y4–y6. Furthermore, the additional variable of the augmented state vector for y5 was able to describe magnitude and signature of the sensor bias, which the lower right plot in Fig. 2 confirms. The fault diagnosis therefore demonstrated that the fault could be detected and correctly diagnosed. Moreover, if this sensor would have been part of a control loop, the corrected measurement could have been used instead of preventing a propagation of this fault. Therefore, this application study demonstrates how the proposed FDI scheme can assist an experienced operator in identifying which sensor is faulty and how to maintain a robust control scheme in the presence of a sensor fault by switching to the reconstructed process value.

Type

Tag

Notation

Unit

Output

y1 , . . . ,y9 y10

Temperatures on tube skins 1, . . . ,9 Temperature of naphtha outlet

1C 1C

4.2. Process fault detection in a distillation column

Input

u1 u2 u3

Naphtha flow Fuel gas pressure Fuel gas flow

m3/h kg/cm2 m3/h

This section summarizes the application of the proposed unified scheme to a distillation process to detect and diagnose a complex process fault. The unit purifies butane (C4) from a feed

104

102

SPEUIO 99% CL

SPEi

SPE

103 102

SPE4 SPE5 SPE6 99% CL

100

101 100 200

300

400

500

10−2 200

600

300

Time [min]

Temperature [°C]

Temperature [°C]

600

500

600

5

495 485

465 200

500

Time [min]

505

475

400

y4 y5 y6 yˆ 5

300

400 Time [min]

500

600

−5 −15 −25 −35 200

ˆ f4 ˆ f5 ˆ f6

300

400 Time [min]

Fig. 2. SPE statistic for sensor fault in skin temperature measurement (top left), fault diagnosis of the biased measurement in sensor 5 (top right), measurement reconstruction with removed fault effect (bottom left) and fault signature estimation (bottom right).

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485

containing a mixture of hydrocarbons. Operational constraints include that the concentration of the heavier component pentane (C5) in the top draw as well as the concentration of lighter component butane in the bottom draw remains below predefined limits. The process is known for reductions in feed flow which, in turn, can result in violations of these operational constraints if severe. The propagation of this disturbance into such a severe process fault results from an interaction of process control structure, controller tuning and operator support. The characteristics of this fault are described first, prior to a discussion of the fault detection and diagnosis capabilities of the proposed FDI scheme. Previous FDI work using MSPC related to this process includes Lieftucht, Kruger, and Irwin (2006) for example.

Table 2 Process variables of the distillation column.

4.2.1. Plant operation The plant, schematically shown in Fig. 3, operates in a closedloop configuration. The composition control structure corresponds to the LV-configuration with a temperature control loop (Skogestad, 2007). The holdup in the reflux drum and the reboiler vessel is controlled using the top and bottom draw. The column pressure is controlled by the coolant flow into the condenser (not measured). The distillate and bottom product concentrations are controlled indirectly through the reflux flow (adjusted by the operator) and the temperature on tray 31. This configuration is known to achieve good performance for composition control. However, it is also sensitive to alterations in the feed flow (Skogestad, 2007). Table 2 presents a list of recorded variables used in this study. From this process, several data sets with suitable variations were recorded at a sampling time of 30 s. A set of around 15.5 h of NOC

(1850 samples) was used for model identification. The established monitoring model was then applied to a second data set containing about 40 h of data describing a severe drop in the feed level for 2 h following a period of a prolonged but moderate decrease in feed level for 3 h. After the first severe drop, the concentration of the heavy component pentane (C5) increased above the tolerable limit for more than 6 h and therefore represents a highly undesired condition.

PC

LC

TI

QI

FI

QI

FI

2 FC

TI

FI

14

TC

31

TI

TI

LC

Fig. 3. Schematic diagram of the debutanizer distillation column with control structure.

Type

No.

Notation

Unit

Output

y1 y2 y3 y4 y5 y6 y7

Temperature tray 2 (top) Temperature tray 14 (feed) Temperature tray 31 (bottom) Bottom product draw Top product draw Temperature reboiler return Reboiler steam flow

1C 1C 1C t/h t/h 1C t/h

Input

u1 u2 u3

Feed flow Feed temperature Reflux flow

t/h 1C t/h

4.2.2. Fault description The feed flow provided by upstream processes has usually a constant mean with little variation. This flow, however, frequently decreases in level by up to 30%. In response, the level controllers in the bottom vessel, distillate drum and the column pressure can compensate this disturbance of the material balance, which the upper plot in Fig. 4 shows. The temperature controller, however, is unable to respond to such events by adequately regulating the energy balance within the column. This is also shown in the upper plot of Fig. 4, which depicts the temperatures on and above the feed stage, y1–y3. These increased almost immediately in response to the feed drop u1. Consequently, the concentration of C5 in the distillate rose above the constraint about 1.5 h after the level dropped substantially around 24 h into the data set. To simplify the presentation, the reflux flow, u3, and the reboiler-return temperature, y6, are excluded from Fig. 4, as they remain constant or do not contribute to the general picture. It should be noted that the measurements (except for the concentrations) in Fig. 4 have been scaled for a better visualization. Moreover, the steam flow, y7, has been shifted by a constant offset of 6. Monitoring the composition measurements only is insufficient, given that any increase in the C5 concentration arises with a delay of around 1.5 h. Moreover, monitoring the absolute feed flow is also insufficient, as a slowly decreasing flow will not have the same negative effects. The plots in Fig. 4 demonstrate that a moderate drop in feed level, e.g. between 21 and 24 h into the data set does not profoundly affect the concentration level. A successful FDI scheme must therefore rely on a model-based approach, which allows a description of this relationship under NOC. More precisely, if future drops occur, the dynamic model can assess whether a significant departure from NOC arises. Referring to the preceding discussion, a slowly decreasing flow gives rise to a departure from the current operating condition but is not likely to cause the same effect upon the concentrations as an abrupt and prolonged drop in feed level. 4.2.3. Model development and fault detection The application of SMI yielded that the inclusion of n ¼8 state variables produced an accurate prediction of the l ¼7 output variables. Accounting for the control structure, illustrated

U. Schubert et al. / Control Engineering Practice 19 (2011) 479–490

Temperature

486

40 30 20 10 0 −10

y1 y2 y3 u2

15

20

25

30

35

10 Flow

6 2 −2 −6

y5

y4

u1

y7

−10 15

20

25

30

35

20

25

30

35

Concentration

2 C3 (Top)

1.6

C5 (Top)

1.2

C4 (Bottom)

0.8 0.4 0 15

Time [hours] 103

80

2

T 99%-CL

101 T2

u2 u1 u3

70 Input Residuals

102

100 10−1 10−2

60 50 40 30 20 10 0

10−3 4

8 12 16 20 24 28 32 36 Time [hours]

4

8 12 16 20 24 28 32 36 Time [hours]

Fig. 4. Disturbance propagation affecting the temperature profiles, flow rates and product concentrations (top), corresponding T2 statistic (lower left) and reconstructed inputs for diagnosis of disturbed energy balance (lower right).

in Fig. 3, the levels in the bottom and reflux drum, and the column pressure were removed from the set of output variables, since they were under feedback control. Different from the analysis in Lieftucht et al. (2006), the tray 31 temperature y3 and the corresponding manipulated variable, reboiler steam flow y7, were selected as output variables since they are highly correlated to the input variables u1–u3. The identification of a state space process model was followed by constructing a Luenberger observer, L, to estimate the states ^ sequences. Using the state estimates xðkÞ, the input vector uðkÞ ¼ ðu1 ðkÞ u2 ðkÞ u3 ðkÞÞT could now be reconstructed by applying Eq. (7). The input residuals were then computed by applying Eq. (8). To establish the T2 statistic and its control limit, the input ^ were computed, followed by estimating SDuDu residuals DuðkÞ using a different reference set. Fig. 4 summarizes the results of applying this monitoring model to a data set describing a severe feed drop. The upper three plots show that the drop in u1 arose 24 h in the data set. The lower left plot in Fig. 4 confirms that the input residuals responded to this drop by producing a constant violation of the control limit T20.01. It is interesting to note that the initial decrease in feed level around 21 h did not result in a substantial upset of the process operation. However, the T2 statistic became sensitive

to the prolonged reduction in feed flow after 24 h and the second substantial decrease in feed level after 32 h. Measured from the initial reduction in feed flow this event was detected with a delay of approximately 10–15 min. It should be noted that this would have given a substantial reduction of delay in warning, given that the actual process control system reacted on the basis of a critical elevation or degradation of individual concentration measurements. This is the major benefit of including a dynamic model into the residual generation and evaluation. 4.2.4. Fault diagnosis One of the difficulties of MSPC methods is the diagnosis of complex fault conditions. In this specific case, the variables that showed the fastest contribution to the deviation were feed flow, as well as top and bottom draw. With some delay, the feed and top tray temperatures showed some contribution, as outlined in Lieftucht et al. (2006). In another analysis using a dynamic MSPC approach to this data, the entire temperature profile was found to be affected (Kruger, Kumar, & Littler, 2007). Previous MSPC-based FDI work on this data focused on detecting feed upsets that went unnoticed by operators and correctly traced the increasing impurity levels back to the feed flow. It is important to note that previous work is restricted to the

U. Schubert et al. / Control Engineering Practice 19 (2011) 479–490

analysis of a single operating point with a constant feed rate. It is also important to note that the upset in the energy balance is, in fact, the root cause. It is therefore imperative to differentiate between a feed drop and its impact upon the energy balance. This is important as the feed flow may show a slight variation that does not affect the energy balance significantly enough to upset the concentration profiles in the top and bottom draw. Hence, focusing on variations of the feed flow is not sufficient for monitoring this process. In general, Buckley, Luyben, and Shunta (1985) highlighted that the feed flow is the main source for disturbing the energy balance within the column. Moreover, other sources of affecting this balance are alterations in the feed temperature and enthalpy. If the feed temperature increases at a constant flow rate, for example as a result of preheating, less heat is required in the reboiler and increased reflux is necessary to maintain the quality level in the top draw composition. Furthermore, if the feed flow is reduced at a constant temperature, less reboiler duty and a reduced reflux flow are required to keep the concentration profile below the predetermined constraints. These causal relations are well known to experienced plant operators. The lower left plot in Fig. 4 gives a timely alarm when the process operation departs from the NOC and the subsequent analysis of the lower right plot yields the root cause for this abnormal event. This plot highlights that a relatively minor contribution came from the feed flow u1 and to an even lesser extent from the reflux u3. The dominant contribution was from the feed temperature u2. The sequences of input residuals therefore suggested that an increase in feed temperature is required to ‘‘correctly’’ describe the measured plant behavior using the identified SMI model. Yielding the feed temperature, however, clearly identifies the disturbed energy balance. More precisely, the increase in reconstructed feed temperature, or input variable u2, compensated for the reduction in the enthalpy provided by the feed stream. Loosely speaking, the model assumed that this hypothetical increase in feed temperature explained the increased level of impurity, as shown in the upper plot in Fig. 4. In summary, the previous MSPC-based FDI of this event identified the drop in fresh feed as the main contributor. As argued above, this is indirectly correct. Instead, the root cause is an upset in the enthalpy balance of the column, which the application of the proposed MBFDI/MSPC could reveal. In a similar fashion to MSPC, the monitoring task only relied on a T2 statistic, which simplifies the monitoring task for the process operator. The unified model-based approach therefore overcomes the problems in MSPC-based FDI and simplifies the monitoring task for MBFDI applications.

487

where the methyl acetate (MeAc) is produced by the reaction of acetic acid (HAc) and methanol (MeOH) supported by a catalyst. Different fault scenarios for this process have been studied in Lieftucht et al. (2009) using a regression-based MSPC approach. These faults are characteristic process faults of which one is analyzed here to present a benchmark for contrasting the performance of the proposed FDI scheme with the results reported in Lieftucht et al. (2009). 4.3.1. Plant operation The plant operates in a semi-batch mode with two catalytic packings in the lower part and an additional separation packing located in the upper part. Fig. 5 presents a schematic diagram of this process. Methanol is provided through an initial holdup in the reboiler and the acetic acid is fed to the column above the upper catalytic packings. Because water accumulates in the reboiler as a heavy fraction from the reaction in Eq. (15), the boiling point of the mixture in the reboiler is permanently drifting. As a consequence, the process does not operate in a steady state mode. However, the composition profiles among the packings show only moderate variations despite this non-stationarity and can, thus, ¨ be omitted from the analyzed operation conditions (Volker, Sonntag, & Engell, 2006). Concerning the product composition in the distillate, this process operates open-loop. The reboiler duty, the reflux preheating and the condenser are under feedback control using regulatory PI controller or switching control to maintain a constant heat flow, a complete condensation or a constant reflux temperature. Because of the reactive distillation, multiple steady state operating points may arise from which only a few are economically feasible. Monitoring the steady state of such systems is pivotal and of significant interest for detecting a deviation from NOC (Forner, 2008).

cooling water

TI TI

1 2

separation packing

FI

3 4

TI

HAc þ MeOH"MeAcþ H2 O;

6

catalytic packings

ð15Þ

TI

TI QI

TI

product TI

8

The section describes the application of the proposed monitoring scheme to a pilot-scale reactive distillation column. This process provides the integrated reaction and separation of methyl acetate. Because of this integration and operation in a semi-batch mode, the dynamic behavior is very complex, as studied with regards to thermodynamic and control aspects (Gesthuisen, ¨ Dadhe, Engell, & Volker, 2002; Schmidt-Traub & Go´rak, 2006). Consequently, any disturbance resulting from an abnormal operation must be avoided. Moreover, a timely detection and diagnosis of fault conditions is essential for appropriate operator intervention. The case studied in this section describes a fault inside the cooling system, which is safety critical for the process operation. The reaction carried out by this process is

TI

5

7

4.3. Process fault detection in a reactive distillation unit

TI FI

TI TI TI

9 TI 10 11 12

TI Tin

TI TI TI

Heat Flow

13 Tout Fig. 5. Schematic diagram of the reactive distillation column with instrumentation.

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¨ advanced controller design (Volker et al., 2006). Therefore the identified SMI model provided a good approximation of causal relationships between the input and output variables (Gertler & Cao, 2004). Using the variables listed in Table 3, the application of SMI suggested the inclusion of n¼ 6 state variables to model the causal relationships between the m ¼6 input and l ¼17 output variables. Compared to the work in Lieftucht et al. (2009), Table 3 shows a slightly different mapping of input and output variables, which is now discussed. The temperature of the boiling holdup in the reboiler has been included as an input variable since it represents the changing composition, due to the accumulation of water. The flow of condensate is also used as an input variable, given that it is proportional to the steam flow through the column (Gesthuisen et al., 2002). In addition to feed flow and reflux ratio the feed temperature and, more important, the coolant inlet temperature are included as an input variable. The coolant flow itself, however, could not be included as it was not measured. As before, the identification of the state space process model was followed by determining a Luenberger observer and the control limits for the T2 statistic. As outlined in the lower left plot in Fig. 6, the T2 statistic violated its control limit about 610 min into the data set, whilst sporadic violations arose around 530, 570 and 580 min. This is diagnosed next.

4.3.2. Fault description The fault analyzed here was an actuator fault in the condenser of the reactive distillation column. The condenser is typically used to control the pressure through the condensation of the rising steam flow and is therefore a safety relevant part in the plant operation. The control objective is an adequate supply of coolant to ensure complete condensation. As shown by this example, however, the coolant flow may fail and, since this flow is not measured, remains unnoticed until the fault propagates through the system. As can be seen from the variable trends in Fig. 6 (top), the effects of this fault were locally restricted to the column head. While the inlet temperature measurement of the coolant remained constant, the coolant outlet and the condensate outlet temperatures increased by about 20 1C. Resulting from the controlled reflux preheating, the temperature of the reflux remained constant although the temperature in the reflux splitter rose. The top temperatures in the splitting section, however, increased and, consequently, the methanol concentration in the condensate increased. This is undesired, since this would affect the yield of the process negatively. 4.3.3. Model development and fault detection Process data including 3.9 h (1400 samples) of operation was used to identify a state space model. This data set described the process in a dynamically excited mode and was generated for

120 Temperature

100 80 60

y1 y2...y12 y13 y14 u2 u3 u4

40 20

Concentration

Flow

0 4 2

u1 u5 u6

0 −2 1

y15 y16 y17

0.5 0 400

104

500

550 Time [min]

2 T 99%-CL

Input Residuals

105

450

T2

103 102 101 100 10−1 400 450 500 550 600 650 700 Time [min]

450 400 350 300 250 200 150 100 50 0 −50 −100 −150 580

600

650

700

u3 u6 u4 u1 u2 u5

600

620 640 660 Time [min]

680

700

Fig. 6. Disturbance propagation affecting the column head (top), corresponding T2 statistic during faulty operation condition (lower left) and fault diagnosis of the coolant fault using reconstructed inputs (lower right).

U. Schubert et al. / Control Engineering Practice 19 (2011) 479–490

Table 3 Process variables of the reactive distillation column. Type

No.

Notation

Unit

Output

y1 , . . . ,y12 y13 y14 y15 y16 y17

Temperatures 1, . . . ,12 Temperature condensate Temperature coolant out Concentration MeOH Concentration MeAc Concentration H2O

1C 1C 1C mol/mol mol/mol mol/mol

Input

u1 u2 u3 u4 u5 u6

Feed flow acetic acid HAc Temperature feed Temperature coolant in Temperature reboiler Reflux ratio Condensate flow

mol/s 1C 1C 1C % mol/s

4.3.4. Fault diagnosis The analysis of this data in Lieftucht et al. (2009) showed that a large number of variables contributed to this event. Section 4.2.4 also confirmed that fault diagnosis using MSPC can identify rather a larger number of variables for complex faults. The six main variables identified with decreasing contribution were condensate temperature, y13, separation section temperatures y1, y2, y3 and, to a lesser extent y12 and the feed temperature u2. The lower right plot in Fig. 6 highlights that two input residuals showed a significant contribution to this event. These are the coolant inlet temperature, which is too low, and the steam flow (respectively, condensate flow), which is too high to explain the observed behavior. This analysis already restricts the root cause of this event to the overhead condenser, since both variables are inputs to this subsystem. In contrast to the MSPC-based analysis, these inputs follow the strict causal relations in a conventional condenser. Given a drastically increased coolant inlet temperature and an only slightly reduced steam flow, the cooling duty inside the condenser is reduced and the coolant outlet temperature is expected to rise significantly. The described effects of a reduced condenser duty can be immediately confirmed by consulting the time-based plots in Fig. 6 (top) and give rise to the possibility of a failing coolant inlet temperature measurement (scenario A) or a decreased coolant flow (scenario B). Subsequently, the root cause is determined, once the operator varies the coolant flow, which will have no effect on the coolant outlet temperature. If a failing sensor would have been the root cause, the outlet temperature would have responded to this action. An experienced operator can therefore use the diagnostic information in Fig. 6 (lower left) to identify (i) that the reduced condenser duty is responsible for the violation of the T2 statistic and (ii) confirm that the failing coolant flow is the root cause of this event by appropriate intervention. The results show, therefore, that the root cause of this event can be traced down before a critical condition arises (due to insufficient cooling).

5. Concluding summary This paper has proposed a unified model-based approach for FDI in complex technical systems. The approach has merged traditional model-based tools with MSPC methods, which led to a unified approach that combines the advantages of both component technologies. To address the difficulties in obtaining mechanistic models of complex dynamic systems, SMI has been integrated into the model-based FDI approach. The utilization of traditional UIOs and input reconstruction has shown (i) that system augmentation with different fault modes allows selective fault diagnosis by

489

unknown input estimation, (ii) that model uncertainty is indicative of detecting faults and (iii) that the reconstruction of system inputs provides useful diagnostic information. In addition to avoiding the need for rigorous process modeling, embedding model-based FDI into the MSPC framework allows the construction of univariate statistics that simplify the monitoring task. Moreover, the multivariate description of correlated residuals allows a robust fault detection in the face of model uncertainty, which has been identified as a problem for modelbased FDI. For detecting and diagnosing sensor faults a bank of UIOs has been utilized, where the model residuals allow the construction of a univariate SPE statistic. For actuator and process faults, an input reconstruction scheme has been proposed that examines the difference between the measured and reconstructed inputs. These input residuals have been taken advantage of by defining a Hotelling’s T2 statistic for fault detection and individual residuals offer a fault diagnosis capability. This paper has also discussed how to apply the proposed FDI scheme to diagnose simultaneous actuator, process and sensor faults. Such cases may not occur frequently, but certainly offer a great potential for future studies on robust FDI. The application studies to three different industrial processes for which sensor faults and various process faults were recorded have shown that each fault could be detected and correctly diagnosed. Comparing the performance of the unified FDI scheme with traditional MSPC fault diagnosis work has yielded that the proposed scheme presented a clearer picture in diagnosing the process faults.

Acknowledgments The authors acknowledge financial support from the German Research Foundation and The Petroleum Institute, Abu Dhabi, U.A.E. We would like to extend our thanks to the Chair of the Institute of Process Dynamics and Operation at the University of Dortmund, Germany, Prof. Dr.-Ing. Sebastian Engell, for providing access to the data used in Section 4.3. Our thanks are also ¨ extended to Dr. Dirk Lieftucht of SMS Siemag AG, Dusseldorf, Germany, and Dipl.-Ing. Christian Sonntag of the Institute of Process Dynamics and Operation for their kind assistance in dealing with issues regarding these data. References Alcala, C. F., & Qin, S. J. (2009). Reconstruction-based contribution for process monitoring. Automatica, 45(7), 1593–1600. Buckley, P. S., Luyben, W. L., & Shunta, J. P. (1985). Design of distillation column control systems. London: Edward Arnold. Chang, S., You, W., & Hsu, P. (1997). Design of general structured observers for linear systems with unknown inputs. Journal of the Franklin Institute, 334(2), 213–232. Ding, S. X. (2008). Model-based fault diagnosis techniques: Design schemes, algorithms, and tools. Berlin: Springer. Ding, S. X., Zhang, P., Naik, A., Ding, E. L., & Huang, B. (2009). Subspace method aided data-driven design of fault detection and isolation systems. Journal of Process Control, 19(9), 1496–1510. Edwards, C. (2004). A comparison of sliding mode and unknown input observers for fault reconstruction. In: Proceedings of the 43rd IEEE Conference on Decision and Control (Vol. 5, pp. 5279–5284). Fang, H., Shi, Y., & Yi, J. (2008). A new algorithm for simultaneous input and state estimation. In American control conference (pp. 2421–2426). Favoreel, W., De Moor, B., & Van Overschee, P. (2000). Subspace state space system identification for industrial processes. Journal of Process Control, 10(2–3), 149–155. Forner, F. (2008). Anfahren von Reaktivrektifikationsprozessen in Kolonnen mit ¨ Berlin. unterschiedlichen Einbauten. Ph.D. thesis, Technische Universitat Fortuna, L., Graziani, M., & Barbalace, N. (2005). Fuzzy activated neural models for product quality monitoring in refineries. In P. Zı´tek (Ed.), Proceedings of the 16th IFAC world congress (Vol. 16). Elsevier.

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