Design of an active fault tolerant control system for a simulated industrial steam turbine

Applied Mathematical Modelling 38 (2014) 1753–1774

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Applied Mathematical Modelling journal homepage: www.elsevier.com/locate/apm

Design of an active fault tolerant control system for a simulated industrial steam turbine Karim Salahshoor a,⇑, Mojtaba Kordestani b a b

Tehran Faculty of Petroleum, Petroleum University of Technology, Iran Power and Control Engineering Dept., Shiraz University, Shiraz, Iran

a r t i c l e

i n f o

Article history: Received 24 August 2011 Received in revised form 8 August 2013 Accepted 20 September 2013 Available online 8 October 2013 Keywords: FTC FDD GPC Fusion Steam turbine

a b s t r a c t An active fault tolerant control (FTC) scheme is proposed in this paper to accommodate for an industrial steam turbine faults based on integration of a data-driven fault detection and diagnosis (FDD) module and an adaptive generalized predictive control (GPC) approach. The FDD module uses a fusion-based methodology to incorporate a multi-attribute feature via a support vector machine (SVM) and adaptive neuro-fuzzy inference system (ANFIS) classifiers. In the GPC formulation, an adaptive configuration of its internal model has been devised to capture the faulty model for the set of internal steam turbine faults. To handle the most challenging faults, however, the GPC control configuration is modified via its weighting factors to demand for satisfactory control recovery with less vigorous control actions. The proposed FTC scheme is hence able to systematically maintain early FDD with efficient fault accommodation against faults jeopardizing the steam turbine availability. Extensive simulation tests are conducted to explore the effectiveness of the proposed FTC performances in response to different categories of steam turbine fault scenarios. Ó 2013 Elsevier Inc. All rights reserved.

1. Introduction The constantly increasing demand for higher productivity has urged industrial companies to pursue new process and automation technologies for competitive advantages. The progression of deployed emerging technologies has provided a wide range of benefits over the earlier operations environments, but they also created new operational issues. The addition of the advanced control applications enabled the control loop counts to climb up, complicating the supervision of the control loops. Hence, it is no longer a trivial task for operators to detect and identify the root cause of probable process upsets in time on their own expertise to assess their performances. This deficiency results in the operators being unable to effectively manage upset conditions, nor operate the plant for maximum profit contribution. Therefore, it is imperative to explore for fault-tolerant control (FTC) methodologies to minimize the loops performance degradations against potential abnormal situations. Significant amount of attention has been devoted to FTC schemes over the last decade [1]. The developed methods can be broadly categorized into passive and active approaches [2,3]. Passive FTC approach fundamentally relies on robustness of the embedded control design strategy to accommodate for the induced faults. The approach is inherently conservative-based and hence may provide inconsistent performances in response to all individual spectrums of probable faults due to their different severities. Active FTC approach presents a more reliable control framework to aim for consistent stability and performance

⇑ Corresponding author. Address: Sattar Khan Ave., Tehran Faculty of Petroleum, Postal Code: 1453953153, Tehran, Iran. Tel.: +98 21 44208054/ 44208055; fax: +98 21 44214222. E-mail addresses: [email protected] (K. Salahshoor), [email protected] (M. Kordestani). 0307-904X/$ - see front matter Ó 2013 Elsevier Inc. All rights reserved. http://dx.doi.org/10.1016/j.apm.2013.09.015

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Nomenclature W weight vector F fusion output ai ith measurement output bi ith largest of a1, ..., an bi ideal outcome Ai, Bi linguistic labels p1, p2, q1, q2, r1 and r2 design parameters lAi ðxÞ, lBi (y) membership functions OLi ith output layer of ANFIS x, y inputs C penalty parameter K kernel Greek letters ni positive slack variables ai support vectors u(.) function for SVM Subscripts SVM support vector machine ANFIS adaptive neuro-fuzzy inference system OWA ordered weighted averaging FTC fault-tolerant control MPC model predictive control GPC general predictive controller ANN artificial neural network FL fuzzy logic NNs neural networks FKB fuzzy knowledge base HP high pressure IP intermediate pressure LP low-pressure DAGSVM directed acyclic graph SVM OAA one against all GRBF gaussian radial basis function MLP multi-layered-perceptron SOM self-organizing map FDD fault detection and diagnosis

objectives via controller reconfiguration on the basis of a priori knowledge of the occurred fault root cause. Therefore, a key element of this motivating FTC approach corresponds to existence of fault detection and diagnosis (FDD) block to recursively provide fast and accurate diagnostic information about the occurrence of a fault, its location and severity size [4]. This can lead to a more reliable control approach to take a proper fault accommodating action following the observation of a fault occurrence. So, every active fault tolerant controller has two main parts; fault detection and diagnosis (FDD) and fault accommodation. Over the last three decades, the growing demand for safety, reliability, maintainability, and survivability in industrial plants has drawn significant research in FDD. An incorrect or much delayed. FDD action may not only result in a loss of system performance, but also instability of overall system. An inappropriate reconfigurable control mechanism based on incorrect FDD information will also lead to poor performance and even the loss of stability of the system [2,3]. Fault indicators can be elaborated on line with available measurements. Fault detection comprises the conception of any relevant symptom from the fault indicators and the consequent evaluation of the time of fault occurrence. Fault diagnosis refers to fault-root discrimination which can be based on an analytical model of the system, representing the normal system behavior in the absence of any fault [5]. This is by no means an easy task to be carried out, especially in non-linear dynamic systems [6], mainly due to the model imprecision, leading to difficulties in making a clear distinction between deviations made by model uncertainty and those imposed by a fault affecting the system or unknown disturbances. This usually necessitates a trade-off to be considered between false alarm rate and missed detection rate. On the other hand, obtaining a sufficiently precise analytical model for complex processes is by no means an easy task to be done and hence other diagnostic approaches must be utilized [7]. Signal processing is a candidate approach to fault diagnosis when an analytical model is not a priori available [8]. Signal characteristics may be explored within time domain methods (e.g., correlation and mean-change), frequency domain

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methods (e.g., spectral analysis), or more sophisticated methods like time–frequency or wavelet analysis [9]. However, the main difficulty corresponds to the way a change in some quantity (e.g., the signal mean, the spectrum, etc.) can be correlated to the characteristic of a particular fault. Classification or pattern recognition approach presents a third alternative category to deal with diagnostic objectives. This approach is mainly based on historical process data or expert knowledge about the system and its corresponding misbehaviors. Relevant symptoms are hence identified to be representative of each type of failure. The relationships between symptoms and faults are then correlated by an appropriate supervised learning when faults are known a priori, for instance by an expert [10]. Fast fault alarm represents one of the most important characteristics for a FDD block. The primary goal for the early diagnosis of fault is to have enough time to take compensatory actions including reconfiguration, maintenance or repair. When a fault is detected and diagnosed, fault accommodation can be carried out by either reconfiguring plant or controller reconfiguration. Model switching is a common way to reconfigure the plant when physical redundancy is available. Once a fault is detected, a new model is selected from a pre-calculated set of linear models. These models have already been calculated around optimal plant operating points. An appropriate model can hence be selected on the basis of the fault information and the informative sensor signal values [11]. However, finding a proper correlation-type relationship to accurately correspond the occurred fault characteristic with a suitable descriptive model is by no means an easy task. Therefore, more research works have been directed on the basis of controller reconfiguration approach. A common scheme utilizes the controller parameters to be retuned in respond to an occurred fault. This scheme, however, necessitates a priori knowledge of human operator to exercise proper changes in controller parameters when a specific fault occurs [12,13]. Recently, more research interest has been motivated to employ artificial intelligence in fault tolerant control. [14] presents a neural network in order to compute a complementary signal to be added to the nominal control signal to deal with a faulty plant. An adaptive neural network model-based fault tolerant control approach is suggested in [15] for unknown non-linear multi-variable dynamic systems. A multi-layer perceptron network is used as the process model and is adapted on-line using an extended Kalman filter to learn changes in process dynamics. In this way, the adaptive model will learn the post-fault dynamics caused by actuator or component faults. Then, the inversion of the neural model is used as a controller to maintain the system stability and control performance after fault occurrence. Steam turbines are widely spread in power plants as the main energy generating sources. They generally possess a complex dynamic structure, incorporating multistage steam expansion processes. A variety of faults can occur in these critical plants during their normal operations. The most common faults of steam turbines occur in steam extractions, feed water heaters, and their related actuators [16,17]. These faults can jeopardize the steam turbine availability by irritating the safety hazards, leading to inconsistency of reliable power generation. Therefore, devising a fault-tolerant control scheme is quite vital to systematically integrate early fault detection and diagnose (FDD) with efficient fault accommodation against any jeopardizing consequence. Despite the critical role of maintaining reliable steam turbine operation to respond to the ever-increasing energy demand, less research attention has been devoted to the issue of fault accommodation or FTC in this area. This paper addresses this important research interest by integrating a data-driven FDD approach [16] and a model-based predictive control (MPC) strategy to make their individual benefits. It is well-known that fault detection and diagnosis (FDD) and fault-tolerant control (FTC) have been the subject of considerable interest in research communities. Thus, many approaches can fundamentally be considered as alternative candidates to devise fault tolerant control scheme for industrial steam turbines. As steam turbines cannot be easily represented using accurate first-principles mathematical models, data-based FDD approaches offer a better alternative to effectively utilize the operational data which are easily accessible from the plant measurement systems. The successful applications of data-driven FDD have been reported in a number of different industries [18]. Neural networks (NNs) and fuzzy logic (FL) systems are among the most powerful data-driven methods for monitoring data pattern classification in diagnostic tasks. NNs can learn to perform the required non-linear mapping through a process of training on many different examples of input/output mapping of interest. The trained NNs, however, are difficult to interpret physically and thus the underlying model remains cryptic. On the other hand, models based on FL scheme exhibit an inherent flexibility which has proven to be successful in a variety of industrial control and pattern recognition tasks [19,20]. FL-based schemes are able to effectively deal with imprecise characteristics of industrial operating data so as to configure them in a fuzzy knowledge-base (FKB) structure in terms of rule format, making them easy to be examined and understood. The main difficulty, however, stands in fuzzy partitioning of the input–output spaces to establish the fuzzy rules, which may require a time-consuming trial and-error process. Moreover, the elicitation of rules from human experts can be an expensive and error-prone procedure. Currently, active research is underway for developing techniques for automatic generation of fuzzy rules from available data. Adaptive Neuro-Fuzzy Inference System (ANFIS) composes the neural and FL approaches to exploit the advantages of both, namely, learning capability and computational power of NN combined with reasoning of fuzzy systems. The result offers an appealingly powerful framework for tackling practical classification problems [21–24]. This technique has emerged as a mean to deal with ‘grey-box’ models with good numerical accuracy and reasonable interpretability [25,26]. An ANFIS classifier is able to create class boundaries that reduce its misclassification rates. Support vector machine (SVM) is considered as a novel machine learning method based on statistical learning theory. It provides a powerful tool for pattern recognition [27] to handle problems having small sampling, nonlinear and high dimension. SVM utilizes a separating hyper plane with maximum margin to produce a good generalization performance by separating different classes. Thus, it provides a unique solution with a strongly regularized characteristic which is quite

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appropriate for ill-posed classification problems. As a consequence, SVM has been widely used for many applications, such as fault detection [28,29] and modeling of nonlinear dynamic systems [30]. New FDD approaches based upon adaptive neurofuzzy inference system (ANFIS) classifier and a fusion-based approach, incorporating a multi-attribute feature via a support vector machine (SVM) and adaptive neuro-fuzzy inference system (ANFIS) classifiers, have been introduced in [16,17]. The work presented in this paper encompasses an elaborate integration of a powerful FDD approach [16] and a new GPC-based fault accommodation methodology to enhance availability of an industrial steam turbine. The utilized FDD approach is based on a new data-fusion scheme to combine the merits of two individual SVM and ANFIS classifiers. The novelty of the proposed FTC methodology is manifested in the way the two main FTC ingredients, i.e. the FDD approach and the GPC-based control design scheme, have been integrated. The GPC is a well-known control method in the MPC family. The method, however, is best practiced for non-faulty circumstances. The new control idea introduced in this work mainly lies on how the FDD block is accommodated in the general FTC framework to communicate and cooperate with the GPC methodology. Further main contribution relates to the way a new GPC-based FTC control scheme has been formulated to efficiently capture the faulty model for the set of internal steam turbine faults to adaptively reconfigure its control structure. Nowadays, data-fusion approach is widely addressed in different fields to enhance decision-making process using a set of informative sources. The synergistic use of overlapping and complementary data sources enables a rich database which is not accessible through individual sources. Therefore, the fused classifier can lead to more precise and reliable results through incorporating complementarities among different classifiers. Once a fault is isolated by the FDD, fault accommodation can be carried out on the basis of the respective faulty plant model. The proposed FTC exploits the diagnostic information to properly adapt an adequate MPC-based controller by changing the values of the weighting factors R and Q for the major faulty situation. Model predictive control (MPC), also referred to as receding horizon control or moving horizon optimal control, has gained widespread attention during recent years [31] with some typical applications in fault tolerant control systems [32]. Model predictive control philosophy is essentially based on the prediction of the future system behavior by using a process model to minimize a certain objective function. The idea of MPC can be traced back to the 1960’s [33], but interest in this field started to surge only in the 1980s after publication of the first papers on IDCOM [34] and Dynamic Matrix Control (DMC) [35,36], and the first comprehensive exposition of Generalized Predictive Control (GPC) [37,38]. The proposed FTC methodology is evaluated on a diverse set of faults scenarios, being introduced in an industrial-based steam turbine simulation case study. The steam turbine represents a 440 MW power plant with once-through Benson type boiler, comprising high, intermediate and low-pressure sections. The paper is organized as follows. Section 2 gives a concise description of steam turbine plant. Section 3 introduces the proposed FTC system for an industrial steam turbine using the integrated fusion-based FDD and a GPC-based control structure. Section 4 presents a diverse set of test scenarios to examine the efficacy of the developed FTC system. Several simulated tests and results are demonstrated in Section 5. Finally, a summary of results is given in Section 6.

2. An industrial steam turbine Steam turbines are the mainstay of electricity production worldwide due to their efficiencies and costs. Steam turbine performance has a remarkable effect on power plant economy. Today’s competitive generation market has increased the pressure to meet the growing requirements for cost-effective and undisturbed operation. A contributing factor in providing ongoing assurance of acceptable plant operation is to integrate steam turbine condition monitoring mechanism in plant control system to ensure continued operation. Because, power plants can no longer afford to operate without knowing the exact steam turbine performance at all times and without taking immediate actions when problems occur. Generally speaking, steam turbines have multistage steam expansion subsections to increase their thermal efficiencies. This might make it difficult to surely predict the effects of any proposing control system on the power plant operations due to the steam turbines structures. Therefore, developing nonlinear analytical models is necessary for the purpose of examining the turbine transient dynamics. These models can be utilized for control system design synthesis, performing real-time power plant simulations and monitoring the plant state variables. The paper uses a valid simulation of an industrial steam turbine, developed by Chaibakhsh and Ghaffari [39], to mimic as a real steam turbine. The corresponding mathematical models have been developed for analysis of the steam turbine transient response subsections based on the energy balance, thermodynamic state conversion and semi-empirical equations. For this purpose, [39] has utilized empirical relations together with an optimization approach based on genetic algorithm to estimate the unknown parameters of models. These parameters correspond to functions describing specific enthalpy for liquid phase and specific entropy in both liquid and vapor phases as typical example, on the basis of experimental data obtained from a complete set of field experiments. In intermediate and low-pressure turbines where steam variables deviate from prefect gas behavior in sub-cooled regions, the thermodynamic characteristics are highly dependent on pressure and temperature of each region. Thus, nonlinear functions have been developed in [39] to evaluate specific enthalpy and specific entropy at these stages of turbines. Accordingly, their relevant parameters have been individually adjusted for matching operational range of each subsection by using genetic algorithm as an optimization approach. The steam turbine represents an industrial 440 MW power plant with once-through Benson type boiler, comprising high, intermediate and low-pressure sections. In addition, the system includes steam extractions, moisture separators, and the

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Fig. 1. Steam turbine and the FDD system and the controller.

Fig. 2. Steam turbine configuration and extractions.

related actuators. Fig. 1 illustrates the simulated steam turbine together with the developed FTC system in terms of the combined FDD block and GPC controller in Matlab-simulink environment. The steam turbine configuration and extractions have been shown in Fig 2. It is noted that HP turbine superheated steam is responsible for energy flow and conversion power in the turbine stages. The superheated steam, at 535 °C and 18.6 MPa, is fed as input to the HP turbine from the main steam header. The input steam pressure drops about 0.5 MPa by passing through the turbine chest system. The inlet steam expands in the HP turbine and then is discharged into the cold reheater line. At full load conditions, the output temperature and pressure of HP turbine become 351 °C and 5.37 MPa, respectively. The cold steam passes through moisture separator to become dry. The extracted moisture goes to HP heater and the cold steam is sent to reheat sections. The reheater consists of two sections where a desuperheating section is allocated between them for controlling the outlet steam temperature. The reheated steam, at 535 °C and 4.83 MPa, is fed to IP turbine. Exhaust steam from the IP-turbine is fed into LP turbine for the last stage expansion. The input temperature and pressure of the LP turbine are 289.7 °C and 0.83 MPa, respectively. Extracted steam from the first and second IP extractions is then sent to HP heater and de-aerator. Also, extracted steam from the last IP and LP extractions are used for feed water heating in a train of LP heaters. The very low pressure steam from the last extraction goes to the main condenser to become cool so as to be used in generation loop again.

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3. Fault tolerant control of an industrial steam turbine A new fault tolerant control (FTC) methodology is presented to automate handling of abnormal situations in an industrial steam turbine. For this purpose, the abnormal situation should first be detected and identified through a FDD block so as to update a GPC-based control system to meet the new requirements caused by the induced fault. Therefore, the main objective of the proposed FTC is to adapt to the changes caused by faults and maintain the steam turbine performance at an acceptable level of operation. This provides enough time for operators and maintenance staff to repair the damage or take alternative measures to avoid catastrophe [40,41]. This section presents the proposed fault tolerant control scheme. First, a fusion-based FDD is developed and then the result will be integrated in the FTC framework to accommodate the faults in control system design on the basis of a GPC-based control structure. 3.1. Fault diagnosis of steam turbine using a fusion-based classification scheme This section introduces the development of the proposed fusion-based classification technique. The basic idea relies on complementary inferences due to each individual ANFIS and SVM classifier. In this scheme, each classifier is trained over the whole operating space and the final decision is then derived through an aggregation space. It is now practically known that it is no longer feasible to set alarm thresholds just on the basis of single measurement devices to detect the faults. This is mainly due to the strong interactions between measurements and subtle changes in correlations between measurements that are correlated to the introduced faults. The proposed fusion procedure is functionally similar to the same intellectual procedure that is often used by operators in the control room. The operational patterns are first recognized and classified into different groups. In this way, different combinations of operational data, representing several possible malfunctions, can be sorted into different groups of pre-determined faults. The ordered weighted averaging (OWA) operator is introduced as the fusion method in the following to integrate the diagnostic inferences due to the individual ANFIS and SVM classifiers. 3.1.1. Ordered weighted averaging (OWA) operator The ordered weighted averaging (OWA) operator, introduced by Yager [42], provides a general class of parameterized aggregation operators including the min, max, and average. Many applications in different areas have been proposed [43–46,16] on the basis of this operator to realize decision making. The major thrust behind selecting the OWA operator to aggregate multi-criteria relates to its inherent capability to encompass a range of operators bounded between minimum and maximum. 3.1.1.1. The OWA operator and its weight generation methods. An OWA operator of dimension n represents a mapping indicated by F:Rn ? R on the basis of an associated weight vector W = (w1, w2, ..., wn)T to satisfy the following:

Fða1 ; . . . ; an Þ ¼

n X wi bi

w1 þ w2 þ    þ wn ¼ 1;

0 6 wi 6 1;

i ¼ 1; . . . ; n;

ð1Þ

i¼1

where a1, ..., an are information sources and b1, ..., bn are the sorted information sources from biggest to smallest. A very crucial issue to apply the OWA operator corresponds to the way its weights are determined. For aggregation purposes, assume that there are M different data, each of them consisting values supplied by N information sources and the correct outcome that is intended to be estimated. Therefore, each example consists of N + 1 values, represented by ai1 ai2 . . . aiN jti for the ith example where aij indicates the value supplied by the jth information source and ti being the ideal outcome for the same example. Hence, the main goal is to find the weighting vector w so that the following error criterion is accomplished: M X 2 Minimize ðWðaj1 ; . . . ; ajn Þ  t j Þ :

ð2Þ

j¼1

There exist several methods to address this problem based upon the cost function to be minimized (e.g., quadratic, convex) and the type of imposed restrictions (e.g., linear constraints, equality constraints). The gradient descent method has been adopted in this research work for implementing the OWA operator [47,48]. 3.1.2. Adaptive neuro-fuzzy inference system (ANFIS) Fuzzy logic performs an inference mechanism under cognitive uncertainty. The cognitive uncertainty associated with the subjectivity of human thinking. For the first time, cognitive uncertainty has been modeled with mathematic function by Zadeh to show human cognitive of uncertainty [49]. On the other hand, computational neural networks are able to offer interesting complementary characteristics including learning, adaptation, fault tolerance, parallelism and generalization. Thus, to enable a system to deal with cognitive uncertainties in a manner more like humans, neural networks have been engaged with fuzzy logic, creating a new terminology called neuro-fuzzy method. Takagi and Hayashi made pioneer

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augmentation in development of neuro-fuzzy technology in 1991 [50]. As the name suggests, ANFIS combines the fuzzy qualitative approach with the neural networks adaptive capabilities to achieve a desired performance. ANFIS represents, in fact, a fuzzy model, configured in the framework of an adaptive system, to facilitate learning and adaptation. Such system can then be trained with qualified data to act correctly under cognitive uncertainty. Fig. 3 illustrates the ANFIS general architecture. For simplicity, a fuzzy inference system with two inputs x and y and one output f has been assumed. For a first-order Sugeno fuzzy model, a common rule set with two fuzzy if-then rules can be defined as: Rule 1: if x is A1 and y is B1, then f1 = p1 x + q1 y + r1 Rule 2: if x is A2 and y is B2, then f1 = p2 x + q2 y + r2 where A1, A2, B1 and B2 indicate the linguistic labels which have been used to define the membership functions. p1, p2, q1, q2, r1 and r2 are design parameters to be determined during the training stage. In the schematic block-diagram representation, a circle indicates a fixed node whereas a square indicates an adaptive node. An adaptive node means that the parameters are changed during adaptation or training. As noted, the architecture consists of a five-layered feed-forward neural structure, where the functionality of the nodes in these layers can be summarized as follows: (1) All the nodes in the first layer are adaptive. Each node in this layer corresponds to a linguistic label and the output equals the membership function of this linguistic label:

OL1i ¼ lAi ðxÞ;

ð3Þ

OL1i ¼ lBi ðyÞ:

(2) The nodes in layer 2 are fixed (not adaptive). Each node in this layer estimates the firing strength (wi) of a rule, which is found from the multiplication of the incoming signal:

OL2i ¼ wi ¼ lAi ðxÞ  lBj ðyÞ:

ð4Þ

(3) The nodes in layer 3 are also fixed nodes. Each node in this layer estimates the ratio (wi) of the ith rule’s firing strength to sum of the firing strength of all rules, j. They perform a normalization of the firing strength from the previous layer. The output of each node in this layer is given by:

wi OL3i ¼ wi ¼ Pi

j¼1 wi

ð5Þ

:

(4) All the nodes in layer 4 are adaptive nodes. The output of each node in this layer is the product of the previously found relative firing strength of the ith rule (normally referred to as defuzzifier or consequent parameters), leading to the following rule:

OL4i ¼ wi fi ¼ wi ðPi X þ qi Y þ r i Þ;

ð6Þ

where pi, qi and ri are design parameters, referred to as consequent parameters, since they deal with the then-part of the fuzzy rule. (5) Layer 5 has only one node, and it performs the function of a weighted summer. It computes the overall output as the summation of all incoming signals from layer 4:

OL5i ¼

P j X wi fi wi fi ¼ Pi : i wi i¼1

ð7Þ

Fig. 3. ANFIS general architecture.

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In the ANFIS architecture, there are two adaptive layers (layers 1 and 4). Layer 1 has modifiable parameters, related to the input membership function. The parameters in this layer are called premise parameters. While, layer 4 has three modifiable parameters (pi, qi and ri), pertaining to the first order polynomial. These parameters are usually called as consequent parameters. The task of the training or learning algorithm for this architecture is to tune all the modifiable parameters so as to make the ANFIS output matching the training data. A training algorithm such as back-propagation or a hybrid learning rule, combining the gradient descent method and the least-squares scheme, is employed to find the optimum values for the parameters of the membership functions and the linear parameters on the fuzzy rules, respectively, in such a way to minimize the error between the input and the output pairs (Table 1). In practice, the available training data set is divided into two portions; one for training, and another for cross validation during training. When performance of the ANFIS, using this cross validation data set, is satisfactory, the training procedure is stopped and the calculated weights are kept unchanged. The ANFIS is then tested further on a third independent data set in order to determine if it has a generalization capability, i.e. if its performance is also satisfactory for previously unknown patterns that were not used during the training phase. 3.1.3. Support vector machine (SVM) classifier SVM presents a relatively new computational learning method based on the statistical learning theory [51]. In applying SVM as a classifier, original input data space is mapped into a high-dimensional dot product space called as feature space. Then, an optimal hyper plane is determined in the feature space to maximize the generalization ability of the resulting classifier. This optimal hyper plane is found by exploiting the optimization theory, and respecting insights provided by the statistical learning theory. SVM classifier has been originally designed for binary classification. Thus, binary SVM is first introduced. Then, a multiclass classifier is reconstructed from binary SVM classifiers. 3.1.3.1. Binary SVM. Support vector machine finds a linear separating hyper plane in the feature space for a two class classification problem. Consider a set of training dataset as follows:{(x1, y1), (x2, y2), ..., (xl, yl)} with xi e Rn, yi e {1, 1} and a feature mapping rule z = /(.):Rn ? H which usually maps the initial raw data set to a higher dimension feature space. The SVM method solves this separation task through the following optimal problem: l X 1 min wT w þ C ni ; 2 i1

ð8Þ

w;n

1

yi ðw /ðxi Þ þ bÞ P 1  ni

;

8i ¼ 1; . . . ; l ; ni P 0;

where C > 0 is a penalty parameter, and ni denotes positive slack variables. This represents a quadratic optimization problem that can be solved using Lagrange multipliers. Therefore, the hyper-plane decision function can be written as:

f ðxÞ ¼ sgn

! m X yi ai :Kðxi ; xj Þ þ b ;

ð9Þ

i¼1

where K(xi, xj) = U(xi).U(xj) Here, the training samples whose ai are non-zero are called as ‘‘support vectors’’ (SV) and the resulting decision function is defined by only these vectors. 3.1.3.2. Multi classifier SVM. SVM has been originally developed to solve binary classification problems. But, practical problems often have classes more than 2. To comply with these practical problems, two types of approaches have been introduced to construct multi-class SVM. One approach is realized by combining several binary SVMs, i.e. implementing multi-class classification based on binary classification. The other approach is implemented by direct multi-class classification. The first approach includes ‘‘One against One’’ (OAO) [52], and ‘‘One against All’’ (OAA) [53] methodologies. In this paper, OAA is used as the main fusion approach. OAA strategy consists of constructing a SVM for each class. This means that one binary support vector classifier is utilized to separate members of a specific class from members of other classes. Therefore, for a C-class classification problem, the one-against-all method constructs C SVM models. As a result, the kth SVM is trained

Table 1 Architecture of the ANFIS models and network’s error. Network

Learning method

Error (MAPE)

ANFIS#1 ANFIS#1 ANFIS#2 ANFIS#2 ANFIS#3 ANFIS#3

Hybrid Back propagation Hybrid Back propagation Hybrid Back propagation

0.04679 1.1141 0.10616 1.4938 0.20196 1.4873

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for the kth class, allocating positive labels for the relevant class members while other classes members are indicated by negative label. 3.2. fault accommodation using generalized predictive control (GPC) approach In this section, a generalized predictive control scheme is developed to accommodate the faults by reconfiguring the controller. 3.2.1. Model predictive control Model predictive control represents the class of advanced control techniques most widely applied successfully in industrial plant [31]. Primary advantages to this approach is the explicit handling of actuator constraints and the straightforward formulations to cater for time-delay problems, multivariable control problems, and hence allowing operation to be run close to constraints, which frequently leads to more profitable operation. The name MPC stems from the idea of employing an explicit model of the plant to be controlled which is used to predict the future output behavior. This prediction capability allows solving optimal control problems online, where tracking error, namely the difference between the predicted output and the desired reference, is minimized over a future horizon, subject to constraints on the manipulated inputs and outputs. The result of the optimization is applied according to a receding horizon philosophy, i.e., only the first input of the optimal command sequence is actually applied to the plant at the present time t. This means that the remaining optimal inputs are discarded, and hence a new optimal control problem is solved at the next time instant (t + 1). As new measurements are collected from the plant at each time t, the receding horizon mechanism provides the controller with the desired feedback characteristics. The tuning of the MPC is based on the selection of the lengths of prediction and control horizons, cost function weighing factors, and the parameters of the noise model included in the internal model of the controller. All the tuning parameters have a logical effect on the behavior of the controller, which makes it quite easy to tune up the controller in a heuristic way. 3.2.2. Development of a fault accommodation based GPC method Fault tolerant control (FTC) maintains a cost effective way to provide dependability as a fundamental requirement in industrial automation. The control system with the ability to continue operating acceptability to fulfill specified functions following faults in the controlled system is defined as a fault tolerant control system [54,55]. There may be some performance degradation during operating under faulty conditions; however the primary objective is to maintain system operation to avoid unexpected trips and outages. Model predictive control (MPC) has already been applied in fault tolerant control systems [32]. Its structure is very suitable for reconfiguration of the control law following the fault occurrence in the controlled system. The control signal is recomputed at each control cycle by solving the optimization problem, leading to opportunity of making appropriate changes in the problem formulation. Moreover, reconfigurable constraints can be included in the optimization cost function to give better possibilities of adapting the control system to meet the new objectives caused by the induced faults. In this paper, generalized predictive controller (GPC) [37,38] is used as a generalized and most common version of MPC family to formulate a fault accommodation controller. In GPC, a common discrete-time model used for output prediction is the so-called controlled auto-regressive integrated moving average (CARIMA) model presented in the following form:

Aðq1 Þ yðtÞ ¼ qd Bðq1 Þ uðt  1Þ þ

fðtÞ ; D

ð10Þ

where u(t), y(t) and f(t) represent control input, output and noise input sequences of the system, respectively. In Eq. (10), A and B are polynomials in the backward shift operator q1 as:

Aðq1 Þ ¼ 1 þ a1 q1 þ a2 q2 þ    þ ana qna ;

ð11Þ

Bðq1 Þ ¼ b0 þ b1 q1 þ b2 q2 þ    þ bnb qnb ;

d and indicate system dead time and the difference operator (1  q1), respectively, in Eq. (10). The GPC cost function can be described as follow:

JðN1 ; N2 ; Nu ; q; rÞ ¼

N2 X

2

^ðt þ jÞ  wðt þ jÞ þ Q ðiÞ½y

j¼N 1

Nu X 2 RðjÞ½Duðt þ j  1Þ ;

ð12Þ

j¼1

where N1 and N2 denote minimum and maximum prediction horizons, Nu is control horizon, Q(j) and R(j) are weighting sequences and w(t + j) is the future reference trajectory. The aim of predictive control is to drive the future control sequence such that the plant output y(t) would meet a desired value in the future. Computing the future tracking errors can be easily achieved by using Diophantine approach. To derive a j-step ahead prediction of model output, y(t + j), the Diophantine equation has the following form:

~ 1 Þ þ qj F j ðq1 Þ; 1 ¼ Ej ðq1 ÞAðq

ð13Þ

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where Ej and Fj are polynomials uniquely defined, given Ã(q1) = A(q1) over the prediction interval j. According to Eqs. (10), (11), and (13), the best predictions of future outputs can be obtained as follows:

^ðt þ jÞ ¼ Gj ðq1 Þ þ Duðt þ j  d  1Þ þ F j ðq1 ÞyðtÞ; y 1

1

ð14Þ

1

where Gj(q ) = Ej(q )B(q ). Here, a complete set of predictions where j runs from a smallest amount to a large value is conˆ(t + j) sidered. These values correspond to the minimum and maximum prediction horizons. For j < t the prediction process y depends on available data, but for j P t some assumption need to be made about future control actions, which are the main key in the GPC. A proposed method to implement long-range prediction is to solve the Diophantine equation recursively. In this case, the polynomials Ej and Fj could be obtained from Eq. (13) as:

Ej ðq1 Þ ¼ ej;0 þ ej;1 q1 þ    þ ej;j1 qðj1Þ ;

ð15Þ

F j ðq1 Þ ¼ fj;0 þ fj;1 q1 þ    þ fj;na qna : Correspondingly, the polynomials for Ej+1 and Fj+1 could be determined by:

F jþ1 ðq1 Þ ¼ fjþ1;0 þ fjþ1;1 q1 þ    þ fjþ1;na qna ;

ð16Þ

Ejþ1 ðq1 Þ ¼ Ej ðq1 Þ þ ejþ1;j qj : As a result, the polynomial Gj+1 is obtained recursively as follows:

Gjþ1 ¼ Ejþ1 B ¼ Gj þ fj;0 qj B; 1

1

ð17Þ 2

where Gj(q ) = gj,0 + gj,1q + gj,2q + . . . . The first j coefficient of Gj+1 are identical to those of Gj and therefore the remaining ones will be given by:

g jþ1;jþ1 ¼ g j;jþ1 þ fj;0 bi

i ¼ 0; . . . ; nb:

ð18Þ

By recalling Eq. (14) for estimating the future outputs of model, the G matrix can be developed of j-term ahead.

8 yðt þ 1Þ ¼ G1 DuðtÞ þ F 1 yðtÞ þ E1 nðt þ 1Þ > > > > > > < yðt þ 2Þ ¼ G2 Duðt þ 1Þ þ F 2 yðtÞ þ E2 nðt þ 2Þ ; : > > > >: > > : yðt þ NÞ ¼ GN Duðt þ N  1Þ þ F N yðtÞ þ EN nðt þ NÞ

ð19Þ

which can be rewritten as:

y ¼ G u þ Fðq1 Þ yðtÞ þ G0 ðq1 Þ þ Duðt  1Þ:

ð20Þ

Then, Eq. (20) can be written in following form:

^ ¼ Gu ~ þ f: y

ð21Þ

Defining reference vector in the following form:

w ¼ ½wðt þ 1Þ;

wðt þ 2Þ;

; wðt þ NÞT :

...

ð22Þ

The cost function expression in Eq. (12) can be written as follows, T J ¼ ðG u þ ~f  wÞ ðG u þ ~f  wÞ þ k uT u Q ðiÞ ¼ 1; RðiÞ ¼ k:

ð23Þ

In this case, minimization of J, when no constraints are imposed on future controls signals, can be obtained by making the gradient of J equal to zero, yielding: 1

~ ¼ ðGT G þ kIÞ GT ðw  f Þ: u

ð24Þ

~ is Du(t), and hence the actual control signal sent to the process u(t) is given by: Noting that the first element of u

uðtÞ ¼ uðt  1Þ þ gT ðw  f Þ; T

ð25Þ T

1

T

where g indicates the first row of ðG G þ kIÞ G . GPC provides a good framework for fault-tolerant control scheme, because, many kinds of failures can be handled online in an adaptive fashion via modifications to the CARIMA model. If the fault is so serious that the original control performance cannot be met, then the FTC methodology should be able to aim for less ambitious control objectives. In this work, elements of the weighting matrices in Eq. (12), i.e., Q(i) and R(i), are chosen as tuning parameters to demand for less stringent control objectives. This approach maintains the stability of the system in major faults by changing the weighting matrices Q(i) and R(i) to recover the system and avoid the plant from emergency shutdowns. In this situation, the desired performance may be lost but the power plant can continue working with satisfactory performance.

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The proposed FTC methodology aims to quickly detect and diagnose fault in the controlled plant and reconfigure the GPC formulation accordingly on the basis of the following reconfiguration schemes: 1. The reconfiguration policy mainly attempts to restore the original control performance in the faulty conditions. For this purpose, the CARIMA dynamic model in Eq. (10) is continuously updated via a recursive least-squares (RLS) identification algorithm to cope with possible internal plant failures, leading to consequent changes in the plant dynamics. 2. In the event of major faults, the GPC control objectives need to be re-tuned as well to give satisfactory control performance. This can be cast as a constrained control problem which in some extent relies on the designer’s experience to moderate the demands made of the plant operation by modifying the individual elements of the weighting matrices in the GPC design objective formulation. The Q matrix is used to weigh the quality of plant control performance in terms of output deviations. Higher values lead to achieve more rigorous closed-loop behavior. The R matrix represents the significant of weights put on controller efforts to achieve the desired control objectives. Higher element of this matrix restricts the controller activities to produce vigorous compensatory actions. 3.3. Steam turbine faults set Three sets of faults have been considered in this research work study. The fault types were inspired from the relevant literature [56–59] and from the experiences of the authors. The proposed FTC is intended to be evaluated on a subset of candidate faults with more emphasis on some typical faults that are difficult to be detected and hence may potentially cause major economic costs. Fault types 1 and 2 (faults 1–3 in Table 2) do not require dismantling of the turbine but can cause plant shutdown or damage of the turbine. Thus, they should be diagnosed early so as to properly be accommodated by the FTC in order to prevent further turbine damaging. Fault type 3 (faults 4 through 12) has been chosen as a typical example of failures that requires dismantling of the turbine for verification and correction, but, it does not cause plant shutdown and hence it only needs to be diagnosed by the FDD to be recovered by the GPC. 3.3.1. Actuator fault This fault affects the actuator performance of the turbine controller. Under the assumption that there are no actuator dynamics in the current turbine model, the actuator fault causes a slower response to the demanded flow rates. Leakage in the safety valve can be due to a broken spindle and hence causes loss of turbine performance [57,60]. 3.3.2. Thermocouple sensor fault This fault represents the malfunctioning of a thermocouple in the turbine steam path which can ultimately lead to a slowly increasing or decreasing reading over time. 3.3.3. Fouling and carry-over in the turbine steam path realized in ‘‘nine cases’’ Fouling originates from impurities in the feed water, entering the steam system and from additives used in water processing. These impurities are transported from the boiler to the superheated steam by three different mechanisms: mechanical carry-over, vaporous carry-over, and attemperators [59,60]. The degree of fouling and depositing is dependent on the boiler pressure level, spraying in super heaters, and other factors [61]. Fouling in the turbine steam path causes degradation of turbine performance. Compounds deposit on different turbine parts, depending on the temperature in the steam path. This fault, in fact, consists of fouling and deposits in stages, extractions and condenser tubes. Fouling stems from residues in district heating water that can build up and insulate the condenser tubes from the inside and thereby reduce heat transfer between the district heating water and the steam. Gassing occurs when non-condensable atmospheric gases form an insulating film on the tubes. This has a considerable impact on heat transfer between the steam and the condenser tubes even at low

Table 2 List of fault types. Fault number

Fault description

1 2 3 4 5 6 7 8 9 10 11 12

Boiler pressure output HP pressure output Steam temperature in HP super heating section Flow rate in the HP-IP line Flow rate in the extraction 1 Flow rate in the extraction 2 Flow rate in the extraction 3 Flow rate in the IP-LP line Flow rate in the extraction 4 Flow rate in the extraction 5 Flow rate in the extraction 6 Flow rate in the condenser

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volume fractions of non-condensable gases [62]. Fouling and gassing reduce the efficiency of the condenser to absorb heat alongside the touching surfaces. Noting that fouling and deposits can be reduced by generally improving the quality of the processed water and by reducing spray in the super heaters. 4. Simulation study A diverse set of test scenarios has been conducted in this section to examine the performance of the proposed FTC system against the preceding three major fault types, being realized in 12 malfunction circumstances listed in Table 2. 4.1. The setup of the simulated process Fig. 1 depicts the overall setup of the simulated process. As shown, the high-pressure steam of the turbine is responsible for energy flow and conversion to power generating in the turbine stages. The superheated steam enters the HP turbine at constant 535 °C from the main steam header. The complete system of the steam turbine has already been explained in details [39]. The generator is assumed to be part of a large interconnected system or be connected to an infinite bus. In order to control the steam turbine, a method of controlling the steam supply is needed. For this purpose, it is assumed that the turbine steam inlet first enters a ‘steam chest’. The steam chest contains a series of steam valves which can be opened gradually as required. As each valve opens, the flow of the stream to the nozzles is increased; leading to higher turbine power. This approach provides for a versatile and economical way to regulate a steam turbine’s power. The proposed fault-tolerant GPC controller allows us to control the mechanical output power of the steam turbine while ensuring the induced constraints to be fulfilled. By developing such controller in an actual system, we can help avoid losses due to mechanical failures that arise from uncontrolled acceleration/speed change in the steam turbine. Furthermore, by optimizing the given cost function we can minimize the amount of energy we need to put into the system to achieve our goal, ultimately reducing the power and energy required to run the steam turbine. 4.2. Fault scenarios The set of faults, considered in this paper is originated from the diverse contributed works reported in the literature for different power plants, being investigated independently by different researches [56–64]. These induced faults have been stimulated through ramp-type functions [63] with an ultimate maximum change of 67 percentages in magnitude. In this simulated test run, each sample time lasts 0.5732 s. In real industrial applications, fouling occurs in several months. However, for the purpose of this simulation study, the fault development rates have been increased in order to avoid excessively long time durations for simulations. The faults have been simulated in ramp-function shapes and consequently the fouling fault scenario was used in a ramp time-base pattern to gradually create a congestion within 30 sample time instants, lasting approximately 17.196 s which was ultimately led to 67 percentage blockage in the pipe. 4.3. Structure of the ANFIS classifier for fault diagnosis In this section, ANFIS networks are used for diagnosis of 12 faults. These faults are divided in three different groups, where each group includes 4 cases of faults and hence one ANFIS network is dedicated to each group of faults leading to 3 ANFIS networks. To achieve an efficient FDD structure, the faults have been organized in the 3 allocated ANFIS’s, on the basis of the faults behavior similarities. Consequently, output of boiler pressure, steam pressure after high pressure section of the turbine, steam temperature in HP super heating section and flow rate in the HP-IP line are dedicated to ANFIS#1, flow rate in the remaining LP and IP extractions have been categorized within ANFIS#2 and ANFIS#3. This fault categorization scheme leads to a much simpler structure for each dedicated ANFIS, leading to more efficient training time. As a consequence, each dedicated ANFIS will have 4 inputs and 1 output as illustrated in Fig. 4. Three generalized bell-shaped membership functions have been assigned to characterize each ANFIS input. Therefore, 81 rules of Sugeno-type (i.e., 34 rules corresponding to 4 ANFIS inputs, each being fuzzified by the three assigned membership functions) are automatically generated by the ANFIS training mechanism for each dedicated ANFIS network. 4.3.1. ANFIS training 13 different data sets are generated through different simulation test runs to be used for the proposed FDD system in the context of the three dedicated ANFISs. These consist of 12 data sets to represent for 12 faulty cases and one set to indicate normal and healthy operation. The resulting ANFIS networks were trained using these data sets via the hybrid training algorithm (Table 1). Different output level ranges were considered for each ANFIS to indicate for different faulty cases. For this purpose, output levels in the ranges of 0.5 to +0.5, 0.5–1.5, 1.5–2.5, 2.5–3.5 and 3.5–4.5 were allocated to the healthy and four faulty cases, respectively. A white noise, having a level of 10% of the actual measurement level, has been added to each plant measurement to infer as the probable measurement noise. To enhance the performance of the proposed FDD system against any miss-alarm condition, occurrence of the three consecution faulty samples has been adopted to surely announce

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Fig. 4. The configured ANFIS architectures.

for a specific known fault. In case, an unknown faulty condition happens outside the dedicated ranges, the proposed FDD system takes it as a novel fault and assigns a level of 2.

4.4. Structure of the SVM classifier for fault diagnosis In this section, a multi SVM classifier is considered for fault diagnostic purposes. Since the real system data has a non-linear characteristic, Gaussian Radial Basis Function (GRBF) kernel is employed to facilitate the classification task. OAA technique is utilized to construct the required multi SVM classifier. 12 types of fault have been considered in this study. Thus, 12 binary SVM classifiers should be designed to diagnose these faults (Table 3). In this case, k-th binary classifier will show positive label if the k-th measurement relates to a faulty condition. Otherwise, the SVM output indicates negative label for the other healthy conditions.

4.5. Structure of the fusion classifier for fault diagnosis Different fault scenarios were conducted to determine the corresponding identification times due to each individual fault by the two ANFIS and SVM classifiers. Table 4 summarizes the obtained results. To calculate the optimal OWA weighting factors for the fusion task, the minimization problem, introduced in Eq. (2), was solved. For this purpose, the gradient– descend method was used to obtain the relevant optimal weight factors as W1 = 0.53 and W2 = 0.47. Having designed the fusion classifier, the resulting identification times for the individual faults have been illustrated in Table 4. A white noise with a magnitude of 10% of the actual measurement level has been added to each plant measurement to infer as the probable measurement noise. This enhances performance of the proposed FDD system against any miss-alarm condition. Furthermore, consistent occurrence of three consecutive faulty samples has been adopted to surely announce for a specific known fault. In a special case, when an unknown faulty condition happens outside the dedicated ranges, the proposed FDD system takes it as a novel fault and hence assigns a level of 2.

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Table 3 Measurements used as inputs for FDD systems. FDD system type

Input measured variables Input No. 1

Input No. 2

Input No. 3

Input No. 4

ANFIS#1

Boiler pressure output

HP pressure output

Flow rate in the HP-IP line

ANFIS#2 ANFIS#3 SVM#1 SVM#2 SVM#3

Flow rate in the extraction 1 Flow rate in the extraction 4 Boiler pressure output Boiler pressure output HP pressure output

SVM#4

Steam temperature in HP super heating section Flow rate in the HP-IP line Flow rate in the extraction Flow rate in the extraction Flow rate in the extraction Flow rate in the IP-LP line Flow rate in the extraction Flow rate in the extraction Flow rate in the extraction

Flow rate in the extraction 2 Flow rate in the extraction 5 HP pressure output HP pressure output Steam temperature in HP super heating section Flow rate in the HP-IP line

Steam temperature in HP super heating section Flow rate in the extraction 3 Flow rate in the extraction 6 – – – –

–

– – – – – – – –

– – – – – – – –

SVM#5 SVM#6 SVM#7 SVM#8 SVM#9 SVM#10 SVM#11 SVM#12

Flow Flow Flow Flow Flow Flow Flow Flow

1 2 3 4 5 6

rate rate rate rate rate rate rate rate

in in in in in in in in

the the the the the the the the

extraction 1 extraction 2 extraction 3 IP-LP line extraction 4 extraction 5 extraction 6 condenser

Flow rate in the IP-LP line Flow rate in the condenser – – –

Table 4 Identification time of incipient fault. Faults

ANFIS classifier

SVM classifier

Fusion classifier

1 2 3 4 5 6 7 8 9 10 11 12

13 18 32 8 12 12 15 12 13 12 12 18

18 26 11 10 10 10 7 10 10 11 11 12

16 24 13 10 11 11 10 11 11 11 11 13

Table 5 Weighing factors for different faulty case. Faults

R

Q

Fault Fault Fault Fault

10 20 1 1

1 1 1 5

(1) (2) (3) (4–12) & normal condition

4.6. Structure of the GPC method for fault accommodation The predictive controller uses steam flow, measured power and set point as the inputs. The control horizon, Q and R parameters, na and nb are treated as the controller adjustable parameters. The controller output is steam flow. The steam flow and the measured power are utilized as the corresponding plant input and output data in structure of the predictive controller to recursively identify the plant CARIMA model (i.e., Eq. (10)) in each sample time. Then, the cost function (i.e., Eq. (12)) is minimized to obtain the adaptive control signal (Eq. (25)). Therefore, the controller will be sensitive to both the input and output plant data to adaptively reconfigure itself through changing the CARIMA model in each sample time, being followed by proper changing of Q and R parameters in case of occurring major faults. When a fault occurs, it will naturally affect the output data of the power plant. The plant CARIMA model is consequently updated, yielding a new control signal adaptation. Once the type of the occurred fault is diagnosed through the FDD, an indicative signal is sent to the predictive controller to be adapted according to Table 5. If the fault belongs to the category of faults 4–12, the predictive controller does not need to change the Q and R parameters and the predictive controller can deal with the fault by recursive

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Fig. 5. Fault diagnosis system output (fault 1).

Fig. 6. Faulty output system(fault 1).

Fig. 7. Output controller (fault 1).

updating of the CARIMA model. In the event of major faults (i.e., faults 1–3), the predictive controller cannot cope with the faulty condition only by adapting the CARIMA model and the R and Q parameters should be adapted as well. Table 5 summarizes the adopted combinations of different weighting factors in R and Q for all the considered fault scenarios. As shown, less ambitious control objectives have been aimed for faults 1 through 3 by choosing Q = 1 to demand for

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Fig. 8. Polynomial A (fault 1).

Fig. 9. Polynomial B (fault 1).

Fig. 10. Fault diagnosis system output (fault 2).

satisfactory control recovery from their consequent failures. However, higher weights have been exercised in R factors for the most difficult faults of 1 and 2 to restrict the GPC from taking vigorous control actions in the face of incorrect measurements.

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Fig. 11. Faulty output system (fault 2).

Fig. 12. Output controller (fault 2).

Fig. 13. Fault diagnosis system output (fault 3).

5. Simulation tests and results Different test scenarios (Table 2) were carried out in this section to illustrate performances of the proposed FTC system. Faults1 through 3 in Table 2 represent the measurement faults. These faults are potentially regarded as the most difficult to

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Fig. 14. Faulty output system (fault 3).

Fig. 15. Output controller (fault 3).

Fig. 16. Fault diagnosis system output (fault7).

deal with. Faults 4 through 12 belong to a category of internal faults in which some parts of the steam turbine plant fail due to fouling phenomenon. However, for brevity, only a limited number of them, corresponding to faults 1–3 and 7, have been demonstrated for evaluation purposes.

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Fig. 17. Faulty output system (fault7).

Fig. 18. Output controller (fault 7).

Fig. 19. Polynomial A (fault 7).

The predictive controller without modifying the Q and R parameters is nominated as ‘‘GPC controller’’ and the predictive controller which modifies the R and Q parameters is called as ‘‘reconfigured GPC controller’’. Thus, the GPC controller is

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Fig. 20. Polynomial B (fault 7).

realized only by updating the CARIMA model in each time step while the reconfigured GPC controller requires simultaneous changes in the CARIMA model and the Q and R parameters in each time instant. Figs. 5–7 depict the results obtained for fault number 1. Fig. 5 represents the FDD system output. Fig. 6 shows the output system, whereas, Fig. 7 presents the output controller. As it can be seen, Fig. 5 clearly illustrates both the detection and diagnostic activities of the three ANFIS, SVM, and fusionbased classifiers. The time when the output comes to level indicated by 2, represents that a fault has been successfully detected at 8, 9, and 8 for the respective classifiers. Then, it took some time later onto be able to diagnose the occurred fault. As shown, this fault has been diagnosed at respective 13, 18 and 16 sample times for the same sequence of indicated classifiers. Figs 6 and 7 show the behavior of the system output and the controller output when the system is affected by fault 1. Due to the changes made in the R and Q parameters of the reconfigured GPC controller, the reconfigure GPC controller has produced a big control signal, forcing the system to go to saturation for a short time interval. However, it is clearly observed that the plant operation is finally managed to be recovered, indicating that the controller is able to successfully address the faulty condition, and the fault consequence has completely been eliminated at 180 s. Figs. 8 and 9 depict the identified parameters of polynomials A and B, following the occurrence of fault number 1. Figs. 10–12 illustrate the results obtained for fault number 2. Observing the obtained result, shown in Fig. 10, demonstrates that the proposed FDD system has correctly diagnosed type of fault at 16, 26 and 24 sample times via ANFIS, SVM and fusion-based classifiers, respectively. It should be mentioned that the FDD system had already been able to detect the occurred fault at 0, 3 and 0 sample times, respectively. Figs. 11 and 12 show the behavior of the system output and the controller output when the system is affected by fault 2. It is clearly observed that once the R and Q parameters are changed in the reconfigured GPC controller, the reconfigure GPC controller produces a big control signal, leading the system to go to saturation for a short time interval. However, it is shown that the proper system operation is finally recovered, indicating that the controller is able to successfully handle the fault at 120 s. Figs. 13–15 illustrate the corresponding results obtained for fault number 3. Observing the obtained result in Fig. 13, verifies that the proposed FDD system has correctly diagnose type of fault at 32, 10 and 13 sample times via ANFIS, SVM and fusion-based classifiers, respectively. It should be mentioned that the FDD system had already been able to detect the occurred fault at 0, 4 and 0 sample times, respectively. Figs. 14 and 15 show the behavior of the system output and the controller output when the system is influenced by fault 3. Due to the changes made in the R and Q parameters of the reconfigured GPC controller, the reconfigure GPC controller has produced a big control signal, saturating the system output for a short time interval. However, it is clearly observed that the plant operation is finally managed to be recovered, indicating that the controller is able to successfully address the induced faulty condition. Fault number 7, indicating fouling in the condenser, has been depicted in Figs. 16–18. Fig. 16 demonstrates the corresponding FDD diagnostic inferences to identify its occurrence after a short time interval. Observing the obtained result, shown in Fig 16, represents that the FDD systems have been able to correctly detect and diagnose the type of fault. Nevertheless, a miss-alarm inference has been declared by the ANFIS classifier in Fig. 16 at its early diagnostic stage. This diagnostic behavior may occur in the early diagnostic stages due to the insufficient available data in the transient condition. Where, the fault type has been incorrectly diagnosed as fault type 8. In contrast, it can be observed that SVM and fusion-based classifiers have been able to diagnose the correct type of fault. Figs. 17 and 18 show the behavior of the system output and the controller output when the system is faced with fault 7. The GPC controller is able to correctly accommodate this fault without changing its weighting factors. Because, this fault does not cause plant shutdown, and hence it is completely accommodated after nearly 130 s. Figs. 19 and 20 depict the time evolution of the identified parameters of polynomials A and B, obtained after occurrence of fault 7.

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6. Conclusions This paper presents an active FTC scheme to accommodate for a diverse set of faults in an industrial steam turbine. For this purpose, a FDD methodology has been incorporated based on fusion of two individual FDD systems in the context of ANFIS and SVM classifiers. The developed FDD system has been tailored and adapted for the steam turbine being faced with 12 major faulty conditions. The considered steam turbine represents an industrial power plant with once-through Benson type boiler which consists of high, intermediate and low-pressure sections. A GPC architecture has been introduced to maintain a desired fault-tolerant feature in the proposed FTC scheme. An adaptive configuration of the GPC internal CARIMA model has been devised to cope with the set of internal steam turbine faults. This enables the steam turbine to successfully restore its original functionality without entering the unsafe condition in the face of faults 4 through 12. The proposed GPC design formulation is able to retune the adjustable elements of weighting factors R and Q to demand for satisfactory control recovery in confrontation with faults 1 through 3 which could cause the steam turbine to shutdown. This facility aims for less ambitious control objective with less vigorous control in the face of more challenging faults. Different simulation test runs were carried out to explore the efficacy of the proposed FTC scheme to deal with diverse fault scenarios. The simulation results were promising and illustrated the excellent performance of the proposed FTC scheme. Acknowledgment The authors would like to thank Ali Chaibakhsh of Iran for their assistance and permission to used steam turbine model. References [1] M.M. Mahmoud, J. Jiang, Y. Zhang, Active Fault Tolerant Control Systems, Springer, 2003. [2] L.F. Mendonqa, J.M.C. Sousa, J.M.G. Sfida Costa, Fault tolerant control using fuzzy MPC, in: IFAC Fault Detection, Supervision and Safety of Technical Processes, Beijing, 2006. [3] S. Saludes Rodil, M.J. Fuente, Fault tolerance in the framework of support vector machines based model predictive control, Eng. Appl. Artif. Intell. 23 (2010) 1127–1139. [4] Y. Zhang, J. Jiang, Bibliographical review on reconfigurable fault-tolerant control systems, Annu. Rev. Control 32 (2008) 229–252. [5] M. Kinnaert, Fault diagnosis based on analytical models for linear and nonlinear systems- a tutorial, in: Proceedings of the IFAC Symposium on Fault Detection, Supervision and Safety for Technical Process, Safe Process, Washington, USA, 2003. [6] J. Chen, R.J. Patton, Robust Model-based Fault Diagnosis for Dynamic Systems, Kluwer academic publishers, 1999. [7] S. Gentil, J. Montmain, C. Combastel, Combining FDI and AI approaches within casual-model-based diagnosis, IEEE Trans. SMC Part B 34 (5) (2004) 2207–2221. [8] M. Basseville, Model-based statistical signal processing and decision theoretic approaches to monitoring, in: Proceedings of the IFAC Symposium on Fault Detection, Supervision and Safety for Technical Process, safe process, Washington, USA, 2003. [9] S. Lesecq, A. Barraud, Arcing fault detection using wavelet transform, in: Fifth IFAC Symposium on Fault Detection, Supervision and Safety of Technical Processes, Safe Process, Washington, USA, 2003. [10] A. Evsukoff, S. Gentil, Recurrent neuro-fuzzy system for fault detection and isolation in nuclear reactors, Adv. Eng. Inf. 19 (2005) 55–66. [11] M.J. Fuente, T. Durán, Fault tolerant control based on multiple linear models in a chemical reactor, in: European Control Conference, Porto, Portugal, 2001. [12] M. Huzmezan, J.M. Maciejowski, Automatic tuning for model based predictive control during reconfiguration, in: Proceedings of the 14th IFAC Symposium on Automatic Control in, Aerospace, 1998. [13] J.M. Maciejowski, Fault-tolerant aspects of MPC, in: IEE Seminar on Practical Experiences with Predictive, Control, February, 2000, pp. 3/1–3/4. [14] H. Wang, Y. Wang, Neural-network-based fault-tolerant control of unknown nonlinear systems, IEE Proc. Part D Control Theory Appl. 146 (5) (1999) 389–398. [15] D.L. Yu, T.K. Chang, D.W. Yu, Adaptive neural model-based fault tolerant control for multi-variable processes, Eng. Appl. Artif. Intell. 18 (4) (2005) 393– 411. [16] K. Salahshoor, M. Kordestani, M.S. Khoshro, Fault detection and diagnosis of an industrial steam turbine using fusion of SVM (support vector machine) and ANFIS (adaptive neuro-fuzzy inference system) classifiers, Energy 35 (2010) 5472–5482. [17] K. Salahshoor, M.S. Khoshro, M. Kordestani, Fault detection and diagnosis of an industrial steam turbine using a distributed configuration of adaptive neuro-fuzzy inference systems, Simul. Modell. Pract. Theory 19 (2011) 1280–1293. [18] W. Hong, C. Tian-You, D. Jin-Liang, B. Martin, Data driven fault diagnosis and fault tolerant control: some advances and possible new directions, Acta Autom. Sin. 35 (6) (2009). [19] S. Chen, Y. Xu, A kind of least squares support vector machines for pattern classification, in: Proceedings of the 6th International FLINS Conference, 2004, pp. 308–313. [20] A. Habbi, M. Zelmat, Design of a fuzzy model-based controller for a drum boiler-turbine system, in: Proceedings of the 6th International FLINS Conference, 2004, pp. 649–654. [21] J. Du, M.J. Er, Fault diagnosis in air-handling unit system using dynamic fuzzy neural network, in: Proceedings of the 6th International FLINS Conference, 2004, pp. 483–488. [22] M. Marseguerra, E. Zio, P. Avogadri, Model identification by neurofuzzy techniques: predicting the water level in a steam generator of a PWR, Prog. Nucl. Energy 44 (3) (2004) 237–252. [23] J.S. Jang, ANFIS: adaptive network-based fuzzy inference systems, IEEE Trans. Syst. Man Cybern. (1993) 665–685. [24] D. Nauck, R.A. Kruse, Neuro-fuzzy method to learn fuzzy classification rules from data, Fuzzy Sets Syst. (1997) 277–288. [25] J.-R.S. Jang, C.-T. Sun, E. Mizutani, Neuro-fuzzy and Soft computing–A Computational Approach to Learning and Machine Intelligence, Prentice Hall, 1997. [26] M. Ayoubi, R. Isermann, Neuro-fuzzy systems for diagnosis, Fuzzy Sets Syst. 89 (1997) 289–307. [27] F. Melgani, L. Bruzzone, Classification of hyper spectral remote sensing images with support vector machines, IEEE Trans. Geosci. Remote Sens. 42 (8) (2004) 1778–1790. [28] W.W. Yan, H. Shao, Application of support vector machine nonlinear classifier to fault diagnoses, in: Proceedings of the Fourth World Congress Intelligent Control and Automation, Shanghai, China, 2002, pp. 2697–2670.

1774

K. Salahshoor, M. Kordestani / Applied Mathematical Modelling 38 (2014) 1753–1774

[29] L.B. Jack, A.K. Nandi, Fault detection using support vector machines and artificial neural networks: augmented by genetic algorithms, Mech. Syst. Signal Process (2002) 373–390. [30] W.C. Chan, C.W. Chan, K.C. Cheung, C.J. Harris, On the modeling of nonlinear dynamic systems using support vector neural networks, Eng. Appl. Artif. Intell. (2001) 105–113. [31] M. Oshima, I. Hashimoto, H. Ohno, M. Takeda, T. Yoneyama, F. Gotoh, Multirate multivariable model predictive control and its applications to a polymerization reactor, Int. J. Control 59 (3) (1994) 731–742. [32] W.-K. Son, O.-K. Kwon, M.E. Lee, Fault tolerant model based predictive control with application to boiler systems, in: Proceeding of IFAC Safe Process, 1997, pp. 1240–1245. [33] C.E. Garcia, D.M. Prett, M. Morari, Model predictive control. Theory and practice, a survey, Automatica 25 (1989) 33S348. [34] J. Richalet, A. Rault, J.L. Testud, J. Papon, Model predictive heuristic control: applications to industrial processes, Automatica 14 (1978) 413–428. [35] C.R. Cutler, B.L. Ramaker, Dynamic matrix control – a computer control algorithm, in: AIChE 86th National Meeting, April, Houston, Texas, USA, 1979. [36] C.R. Cutler, C.L. Ramaker, Dynamic matrix control—a computer control algorithm, in: Proceedings of Automatic Control Conference, San Fransisco, 1980. [37] D.W. Clarke, C. Mothadi, P.S. Tuffs, Generalized predictive control—part I. The basic algorithm, Automatica 23 (1987) 137–148. [38] D.W. Clarke, C. Mothadi, P.S. Tuffs, Generalized predictive control—part II. Extensions and interpretations, Automatica 23 (1987) 149–160. [39] A. Chaibakhsh, A. Ghaffari, Steam turbine model, Simul. Modell. Pract. Theory (2008) 1145–1162. [40] J. Chen, R.J. Patton, Robust Model Based Fault Diagnosis for Dynamic Systems, Kluwer Academic publishers, Boston, 1999. [41] M. Blanke, M. Kinnaert, J. Lunze, M. Staroswiecki, Diagnosis and Fault-Tolerant Control, Springer, 2003. [42] R.R. Yager, On ordered weighted averaging aggregation operators in multi criteria decision making, IEEE Trans. Syst. Man Cybern. (1988) 183–190. [43] X. Liu, Some properties of the weighted OWA operator, IEEE Trans. Syst. Man Cybern. Part B (2006) 118–127. [44] V. Torra, OWA operators in data modeling and residentification, IEEE Trans. Fuzzy Syst. 12 (2004) 652–660. [45] R.R. Yager, J. Kacprzyk, The Ordered Weighted Averaging Operators—Theory and Applications, Kluwer academic publishers, Dordrecht, 1997. [46] R.R. Yager, OWA aggregation over a continuous interval argument with applications to decision making, IEEE Trans. Syst. Man Cybern. Part B (2004) 1952–1963. [47] D.P. Filev, R.R. Yager, Learning OWA operator weights from data, in: Proc, 3rd IEEE Conf. Fuzzy System, Orlando, FL, (1994) pp. 468–473. [48] D.P. Filev, R.R. Yager, On the issue of obtaining OWA operator weights, Fuzzy Sets Syst. 94 (1998) 157–169. [49] L.A. Zadeh, Fuzzy Sets, Inf. Control 8 (1965) 338–353. [50] H. Takagi, I. Hayashi, Artificial neural network driven fuzzy reasoning, J. Approx. Reason. (1991) 191–212. [51] V.N. Vapnik, The Nature of Statistical Learning Theory, Springer-Verlag, New York, 1999. [52] S. Knerr, L. Personnaz, G. Dreyfus, Single-layer learning revisited: a stepwise procedure for building and training a neural network, in: J. Fogelman (Ed.), Neuro Computing: Algorithms, Architectures and Applications, Springer-Verlag, New York, 1990. [53] C.W. Hsu, C.J.A. Lin, Comparison of methods for multiclass support vector machines, IEEE Trans. Neural Networks 13 (2) (2002). [54] R.J. Patton, Fault tolerant control: the 1997 situation, in: IFAC Safe Process Conference, Hull, UK, 1997, pp. 1033–1054. [55] M. Blanke, C. Frei, F. Kraus, R.J. Patton, Staroswiecki M. What is fault-tolerant control? in: Proc. of IFAC Symp. On Safe Process, Budapest, Hungary, June 2000, pp. 40–51. [56] C.P. Bellanca, IEEE Trans. Energy Convers. 3 (1988) 249–253. [57] M. Genrup, On Degradation and Monitoring Tools for Gas and Steam Turbines (Ph.D. Thesis), Lund University, 2005. [58] J. Kubiak, A. Garcı´a-Gutiérrez, B. Urquiza, The diagnosis of turbine component degradation. case stories, Appl. Therm. Eng. (2002). [59] R. Svoboda, M. Bodmer, Deposits and corrosion in steam turbines, in: ABB power generation TEZ 87–20, paper presented at Ringhals, Sweden, 1987. [60] J.H. Bulloch, A.G. Callagy, Malfunctions of a steam turbine mechanical control system, Eng. Fail. Anal. (1995) 235–240. [61] A. Whitehead, K.T. Sullivan, Carryover and its effects on efficiency, operation and maintenance of industrial steam turbines, Pulp Pap (1983) 309–313. [62] O. Lyle, The Efficient Use of Steam, Her Majesty’s Stationery Office, UK, 1958. [63] S. Simani, C. Fantuzzi, Dynamic system identification and model-based fault diagnosis of an industrial gas turbine prototype, Mechatronics (2006) 341–363. [64] J.M. Maciejowski, N.J. Colin, MPC fault-tolerant flight control case study: flight 1862, in: IFAC Safe Process Conference, Washington, DC, June 2003.