Get 20M+ Full-Text Papers For Less Than $1.50/day. Start a 14-Day Trial for You or Your Team.

Learn More →

Robust Fuzzy Fault Detection and Isolation Approach Applied to Surge in Centrifugal Compressor Modeling and Control

Robust Fuzzy Fault Detection and Isolation Approach Applied to Surge in Centrifugal Compressor... Fuzzy Inf. Eng. (2010) 1: 49-73 DOI 10.1007/s12543-010-0037-6 ORIGINAL ARTICLE Robust Fuzzy Fault Detection and Isolation Approach Applied to Surge in Centrifugal Compressor Modeling and Control Ahmed Hafaifa · Kouider Laroussi· Ferhat Laaouad Received: 1 October 2009/ Revised: 30 January 2010/ Accepted: 6 February 2010/ © Springer-Verlag Berlin Heidelberg and Fuzzy Information and Engineering Branch of the Operations Research Society of China 2010 Abstract This work presents the results of applying an advanced fault detection and isolation technique to centrifugal compressor; this advanced technique uses physics models of the centrifugal compressor with a fuzzy modeling and control solution method. The fuzzy fault detection and isolation has become an issue of primary im- portance in modern process engineering automation as it provides the prerequisites for the task of fault detection. In this work, we present an application of this approach in fault detection and isolation of surge in compression system. The ability to detect the surge is essential to improve reliability and security of the gas compressor plants. We describe and illustrate an alternative implementation to the compression systems supervision task using the basic principles of fuzzy fault detection and isolation asso- ciated with fuzzy modeling approach. In this supervision task, the residual generation is obtained from the real input-output data process and the residual evaluation is based on fuzzy logic method. The results of this application are very encouraging with rel- atively low levels of false alarms and obtaining a good limitation of surge in natural gas pipeline compressors. Keywords Compression system· Centrifugal compressor· Fuzzy modeling· Fuzzy control· Fuzzy fault detection and isolation· Surge phenomena· Supervision system 1. Introduction The compression systems are used in a wide variety of applications [2, 4, 9, 21]. These includes turbojet engines used in aerospace propulsion, power generation using industrial gas turbines, turbocharging of internal combustion engines, pressurization of gas and fluids in the process industry, transport of fluids in pipelines and so on. Ahmed Hafaifa () · Kouider Laroussi · Ferhat Laaouad Industrial Automation and Diagnosis Systems Laboratory, Science and Technology Faculty, University of Djelfa, 17000, DZ Algeria email: hafaifa@hotmail.com 50 Ahmed Hafaifa · Kouider Laroussi · Ferhat Laaouad (2010) These manufacturers are greatly interested with any improvement in performance, life and weight reduction without loss of reliability. Therefore, it is worthwhile to carefully estimate the reliability of rotating systems in order to improve the supervi- sion and the control system or eventually modify the design. Reliability analysis of the supervision structure require some information on the model of the compression system. We know it is difficult to obtain the mathematical model for a complicated mechanical structure. The turbo compressor is considered as a complex system where many modeling and controlling efforts have been made [14]. In regard to the complexity and the strong non linearity of the turbo compressor dynamics, and the attempt to find a simple model structure which can capture in some appropriate sense the key of the dynamical properties of the physical plant, we pro- pose to study the application possibilities of the recent supervision approaches and evaluate their contribution in the practical and theoretical fields consequently. Fac- ing to the studied industrial process complexity, we choose to make recourse to fuzzy logic for analysis and treatment of its supervision problem owing to the fact that these technique constitute the only framework in which the types of imperfect knowledge can jointly be treated (uncertainties, inaccuracies,··· )offering suitable tools to char- acterize them. In the particular case of the turbo compressor, these imperfections are interpreted by modelling errors, the neglected dynamics and the parametric vari- ations. This work presents the results of applying an advanced fault detection and isola- tion technique to centrifugal compressor; this advanced technique uses physics mod- els of the centrifugal compressor with a fuzzy modeling and control solution method. The technique automatically finds the best fault scenario to match measured (or test) data. The best fault scenario provides information about parameter deviations (i.e., fault detection) and fault-contributing components (i.e., isolation). The technique is independent of the thresholds used in fault detection as in some other techniques. The technique is effective even under the condition where data are scarce and widely spaced in time. Operational data from the gas compression station of SONATRACH, SC in Algeria. The purpose of the data is to apply the fuzzy model-based fault iden- tification expertise to industrial gas pipeline. The investigation was conducted with extremely limited knowledge of the compression system and their maintenance his- tories. The measured variables, provided in the data set, only include surge, speed, exhaust temperature, flow, and compressor discharge pressure. With these limited compression system data, we modified an existing, generic model for centrifugal compressor and developed the fuzzy method to “hunt” for suspicious fault states. The detection results were confirmed by the method of validation. The detection ac- curacy of this technique can be improved with additional data and knowledge about the centrifugal compressor. This technique can be readily generalized to fault/state detection of other types of centrifugal compressor in all industries. The presented approach is based on the use of the fuzzy model. As was introduced in [23], by applying a Takagi-Sugeno (TS) type fuzzy model with interval param- eters, one is able to approximate the upper and lower boundaries of the domain of functions that result from an uncertain system. The fuzzy model is therefore intended for robust modelling purposes; on the other hand, studies show it can be used in fault Fuzzy Inf. Eng. (2010) 1: 49-73 51 detection as well. The novelty lies in defining of confidence bands over finite sets of input and output measurements in which the effects of unknown process inputs are already included. Moreover, it will be shown that by data pre-processing the fuzzy model parameter-optimization problem will be significantly reduced. By calculating the normalized distance of the system output from the boundary model outputs, a nu- merical fault measure is obtained. The main idea of the proposed approach is to use the fuzzy model in a Fault Detection and Isolation (FDI) system as residual genera- tors, and combine the fuzzy model outputs for the purpose of fault isolation. Due to data pre-processing, the decision stage is robust to the effects of system disturbances. This paper presents a new method for fault diagnosis of a compression system. The method determines performance indices using fuzzy FDI approach. Firstly, we describe the case study of surge in gas compression system in Section 2. Secondly in Section 3, by using fuzzy modeling in FDI for the compression system control, the proposed method can achieve high performance in the surge control of the compres- sion system. In Section 4, this work illustrates an alternative implementation to the compression systems supervision task using the basic principles of model-based FDI associated with the self-tuning of surge measurements with subsequent appropriate corrective actions. Using a combination of fuzzy modeling approach makes it possi- ble to devise a fault-isolation scheme based on the given incidence matrix. After that in Section 5, followed by experimental results that confirm the effectiveness of the proposed approach in the application results section. In its final part the paper gives some conclusions about this application. 2. Gas Compression System The complex models for surge in centrifugal compression systems have been pro- posed by many authors [5, 10, 12, 22]. An essential step in model-based controller design is to understand the physical phenomena in the system and to develop a math- ematical model that describes the dynamics of the relevant phenomena. In this work, the examined compression system is modeled with just three components. The first component is the inlet duct that allows infinitesimally small disturbances at the duct entrance to grow until they reach an appreciable magnitude at the compressor face. The second component is the compressor itself, modeled as an actuator disk, which raises the pressure ratio by doing work on the fluid. The third component is the plenum chamber (or diffuser) downstream, which acts as a large reservoir and re- sponds to fluctuations in mass flow with fluctuations in pressure behind the actuator disk. In this paper, we are considering a compression system consisting of a centrifu- gal compressor, Close Coupled Valve (CCV), compressor duct, plenum volume and a throttle. The throttle can be regarded as a simplified model of a turbine [4, 6, 12]. The gas turbine installation used in our application for studies of compressor surge detection and control is shown in Fig. 1. 52 Ahmed Hafaifa · Kouider Laroussi · Ferhat Laaouad (2010) Fig. 1 Compression system 2.1. Surge in Centrifugal Compressor Centrifugal compressors will surge when forward flow through the compressor can no longer be maintained, due to an increase in pressure across the compressor, and a momentary flow reversal occurs. Once surge occurs, the reversal of flow reduces the discharge pressure or increases the suction pressure, thus allowing forward flow to resume again until the pressure rise again reaches the surge point [10]. Surge is characterized by large amplitude fluctuations of the pressure and by unsteady, but circumferentially uniform, annulus-averaged mass flow. This essentially one dimen- sional instability affects the compression system as a whole and results in a limit cycle oscillation in the compressor map. This surge cycle will continue until some change is made in the process or compressor conditions. Fig. 2 shows a pressure trace for a compressor system, which was initially operated in a steady operating point. By throttling the compressor mass flow, the machine is run into surge. This figure illus- trates the difference between pressure variations before and after surge initiation. A surge controller typically measures a function of pressure rise versus flow. The con- troller operates a surge valve to maintain sufficient forward flow to prevent surge [4, 5, 7, 8, 11]. The optimum flow rate may be calculated from a simple graph of pressure differ- Fuzzy Inf. Eng. (2010) 1: 49-73 53 Fig. 2 Surge mode in centrifugal compressor Fig. 3 Compressors characteristic curves ence against flow, as shown on Fig. 3. The position of the lines is unique to a par- ticular compressor. The operating setpoint is at the minimum flow rate and pressure difference which avoids surge conditions. The application fuzzy logic for anti-surge control provides a fine and reliable control mechanism maintaining the process close to this setpoint. Many papers and texts on anti-surge control maintain that the onset of surge can occur in as little as 50ms [6, 12, 13, 18]. They then conclude that this, and the requirement for very ”tight” tuning, implies that a digital anti-surge controller must have an extremely fast repeat time. Compressor users, however, point out that the 54 Ahmed Hafaifa · Kouider Laroussi · Ferhat Laaouad (2010) blow off or recycle valve driven by the controller is unlikely to open in less than 2 seconds. The process automation anti-surge control fuzzy logic has been proven to successfully meet the above criteria with repeat times of 75 to 100 ms. 2.2. Centrifugal Compressor Model The resulting equations of the dynamics of the compression system in the model used for controller design are in the form: kP ⎪ 01 P = m− k P − P , ⎪ p t p 01 ρ V ⎪ 01 p ⎡ ⎤ ⎪ 4(k−1) ⎢ k ⎥ ⎪ ⎢ ⎥ A Δh ⎨ ⎢ ⎥ 1 ideal ⎢ ⎥ ⎢ ⎥ m = P 1+η (m, N) − P , (1) ⎪ ⎢ 01 i p⎥ ⎣ ⎦ L C T ⎪ c p 01 η m C ΔT ⎪ 1 t tur p,t tur N = − 2r σπN | m | , 2Jπ 2πN where P is the plenum pressure, K is a numerical constant, P is the ambient pres- p 01 sure,ρ is the inlet stagnation density, V is the plenum volume, m is the compressor 01 p mass flow, k is a parameter proportional to throttle opening, A is the area of the t 1 impeller eye (used as reference area), L is the length of compressor and duct, η is c i the isentropic efficiency, N is the spool moment of inertia, Δh is the total specific ideal enthalpy delivered to fluid, c is the specific heat capacity at constant pressure, c is p v the specific heat capacity at constant volume, T is the inlet stagnation temperature and k is the ratio of specific heats k = . Moore and Greitzer model in [19] gives rise to three ordinary differential equa- tions, the first for the non-dimensional total-to-static pressure riseΔp across the com- pression system, the second for the amplitude of mass flow rate fluctuations m, and the third for the non-dimensional, spool moment of inertia. In the following, and based on the work of Moore and Greitzer model we used the two first equations of (1) equivalent to the model of [4]. The linearization of this model given by [2] around a point of operation M (P , m , u , u )give: pc0 c0 t0 b0 ⎡ ⎤ ⎡ ⎤ ⎡ ⎤ ⎡ ⎤ ⎢ ˆ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ P ⎥ ⎢ B −B ⎥ ⎢ P ⎥ ⎢ 0 ⎥ pC pC ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ x = ⎢ ⎥ = ⎢ ⎥ ⎢ ⎥ + ⎢ ⎥ u ˆ . (2) ⎣ ⎦ ⎣ ⎦ ⎣ ⎦ ⎣ ⎦ b 1 1 V m ˆ m − c c B Bm te B With: t= tw ou ` w it is the frequency of HELMHOLTZ defined by the following H H A B equation: w = a , with a = γRT and B = . The parameters B and G is H a m V L G P C U L A t t C defined by the following equations: B = and G = , B it is the parameter of 2w L L A H c C t stability of GREITZER [9]. 3. Fuzzy Modeling The fuzzy modeling, which directly uses fuzzy rules, is the most important applica- tion in fuzzy theory [23]. Using a procedure originated by Mamdani in the late 70s, three steps are taken to create a fuzzy model for the compression system [23]: Fuzzy Inf. Eng. (2010) 1: 49-73 55 • First, fuzzification (using membership functions to graphically describe a situ- ation). • Second, rule evaluation (application of fuzzy rules). • Third, defuzzification (obtaining the crisp results). Step 1 First of all, the different levels of output (throttle opening, the pressure coefficient and the mass flow coefficient) of the compression system are defined by the triangle membership functions for the fuzzy sets. Step 2 The next step is to define the fuzzy rules. The fuzzy rules are merely a series of if-then statements as mentioned above. These statements are usually derived by an expert to achieve optimum results. The actual value belongs to the fuzzy set zero to a degree of 0.75 for “Pressure coefficient” and 0.4 for “Mass flow coefficient”. Hence, since this is an AND operation, the minimum criterion is used, and the fuzzy set approximately zero of the variable “The throttle opening” is 0.4. Step 3 The result of the fuzzy modeling so far is a fuzzy set. To choose an ap- propriate representative value as the final output (crisp values), defuzzification must be done. This can be done in many ways, but the most common method used is the center of gravity of the fuzzy set. Fuzzy models are flexible mathematical structures that, in analogy to nonlinear models, have been recognized as universal function approximators [1, 3, 23]. Fuzzy models use ‘If-Then’ rules and logical connectives to establish relations between the variables defined for the model of the system. For the given example, let the system to model be the relation between surge and the fluctuations in the mass flow coefficient ΔΦ and pressure coefficient ΔΨ. Thus, in fuzzy modeling the fuzzy ‘If-Then’ rules take the form: I f u is surge then y is High. (3) The fuzzy sets in the rules serve as an interface amongst qualitative variables in the model, and the input and output numerical variables. The fuzzy modeling approach has several advantages when compared to other nonlinear modeling techniques; in general, fuzzy models can provide a more transparent representation of the system under study, maintaining a high degree of accuracy. 3.1. Fuzzy TS Models Developing mathematical models for nonlinear systems can be quite challenging. However, TS fuzzy systems are capable of serving as the analytical model for non- linear systems due to its universal approximation property, that is, any desired ap- proximation accuracy can be achieved by increasing the size of the approximation structure and properly defining the parameters of the approximators [20, 23]. A TS fuzzy system can be defined by: 56 Ahmed Hafaifa · Kouider Laroussi · Ferhat Laaouad (2010) g (x)μ (x) i i ⎪ i=1 y = F (x,θ) = , ts ⎪ R ⎪ μ (x) i=1 (4) g (x) = a + a x +···+ a x , ⎪ i i,0 i,1 1 i,n n ⎛ ⎞ ⎛ ⎞ ⎪ n ⎜ ⎟ ⎜ ⎜ x − c ⎟ ⎟ ⎪ 1 ⎜ ⎜ j ⎟ ⎟ ⎜ ⎜ ⎟ ⎟ ⎜ ⎜ ⎟ ⎟ μ (x) = exp ⎜ − ⎜ ⎟ ⎟ , ⎪ i ⎜ ⎝ ⎠ ⎟ ⎪ i ⎝ ⎠ j=1 where y is the output of the fuzzy system, x = [x , x ,··· , x ] holds the n inputs, 1 2 n i = 1, 2,··· , R represent R different rules, and j = 1, 2,··· , n represent n different inputs, the shapes of the membership functions are chosen to be Gaussian, and center- average defuzzification and product are used for the premise and implication in the structure of the fuzzy system. The g (x) are called consequent functions of the fuzzy system, where a are linear parameters. The premise membership functions μ (x) i, j i are assumed to be well defined so that μ (x)  0. The parameters that enter in i=1 i i a nonlinear fashion are c and σ , which are the centers and relative widths of the j j th th membership functions for the j inputs and i rules. The TS fuzzy model consists of representing the base rules as follows: R : If u is A then y = f (u), i = 1, 2,··· , K, (5) i i i where R denotes the i h rule, K is the number of rules, u is the antecedent variable, y is the consequent variable and A is the antecedent fuzzy set of the i h rule. Each rule i hasadifferent function f yielding a different value for the output y . The most i i simple and widely used function is the affine linear form: R : If u is A then y = a u+ b, i = 1, 2,··· , K, (6) i i i where a is a parameter vector and b is a scalar offset. i i 3.2. Fuzzy Models of Compression System The fuzzy logic model is a rule-based system that receives information fed back from the plant’s operating, in this case the normalized fluctuations ofΦ andΨ. These crisp values are fuzzified and processed using the fuzzy knowledge base [1, 3, 20, 23]. The fuzzy output is defuzzified in throttle and the CCV gains in order to control the plants operating conditions. A fuzzy system involves identifying fuzzy inputs and outputs, creating fuzzy membership functions for each, constructing a rule base, and then deciding what action will be carried out. The response of the system is used to model the control system. Increasing either the throttle gainγ or CCV gainγ will stabilize the system with a penalty of pressure T V lost across the plenum. The fluctuations of the mass flow coefficientΔΦ and pressure coefficientΔΨ are normalized before being sent to the fuzzy model as the crisp input by the following [13, 14, 15, 16]: Fuzzy Inf. Eng. (2010) 1: 49-73 57 |Ψ −Ψ | i i+Δt ΔΨ = , (7) max(Ψ,Ψ ) i i+Δt |Φ −Φ | i i+Δt ΔΦ = . (8) max(Φ,Φ ) i i+Δt Samples of the coefficients are taken at regular time-step intervals, Δt = kh where k is a constant and h is the Runge-Kutta time step size. The crisp output from the fuzzy model adjusts both control gains by the following: γ = γ +γΔγ. (9) i+Δt i i i For the case of two inputs and one output, the rule base is constructed by creating a matrix of options and solutions. The matrix has the input variable along the top side. The entries in the matrix are the desired response of the system, the changes in either throttle or CCV gain. The rule base of three rules can be created: 1) If [ΔΨ is Low] or [ΔΦ is Low], then [Δγ and Δγ is Low]; V T 2) If [ΔΨ is Medium] or [ΔΦ is Medium], then [Δγ and Δγ is Medium]; V T 3) If [ΔΨ is High] or [ΔΦ is High], then [Δγ and Δγ is High]. V T The results of two simulations are presented in this section. The first is the compar- ison between the complex model, the linearized model and the fuzzy model suggested with Greitzer parameter B = 1.50 for the masse flow coefficient, and the second sim- ulation is the comparison between the complex model, the linearized model and the fuzzy model suggested with Greitzer parameter B = 0.50 for the pressure coefficient. For both simulations the value of J, the squared amplitude of rotating stall was set to zero, and the throttle gain was set so that the intersection of the throttle line and the compressor characteristic is located on the part of the characteristic that has a positive slope. The response of the system with comparison is shown in Fig. 4 for the mass flow coefficient for B = 0.50, the response of the system with comparison for the pressure coefficient for B = 0.50 is shown in Fig. 5. Both simulations push the design point along the compressor characteristic until it reaches a stable operation point without overshooting a stable equilibrium point. An overshoot of the equilibrium conditions would result in pressure lost across the throttle. 58 Ahmed Hafaifa · Kouider Laroussi · Ferhat Laaouad (2010) Fig. 4 Response of complex model, linearized model and fuzzy model for the mass flow coefficient with B = 0.50 Fig. 5 Response of complex model, linearized model and fuzzy model for the pressure coefficient with B= 0.50 The response of the system with comparison is shown in Fig. 6 for the mass flow coefficient for B = 1.50, the response of the system with comparison for the pressure coefficient for B= 1.50 is shown in Fig. 7. According to the above figures, we can notice that our fuzzy logic model is very Fuzzy Inf. Eng. (2010) 1: 49-73 59 Fig. 6 Response of complex model, linearized model and fuzzy model for the mass flow coefficient with B= 1.50 Fig. 7 Response of complex model, linearized model and fuzzy model for the pressure coefficient with B = 1.50 reliable since its outputs match those of the nonlinear complex model with a very small error in a short time interval for the open loop response, hence the obtained model can be used for the output prediction or for the compressor control. Accord- 60 Ahmed Hafaifa · Kouider Laroussi · Ferhat Laaouad (2010) ing to the obtained results it appears clearly that the characteristics of the system of compression describes by the complex model reproduced perfectly by the fuzzy logic model. 4. Compression System Control Based on Fuzzy FDI Fuzzy FDI method defining the surge point over a wide range of changing conditions makes it possible to set the control line for optimum surge protection without unnec- essary re-cycling. This method automatically compensates for changes in pressure rise, mass flow, temperature, and compressor rotor speed. The system utilizes a char- acterization of compression ratio versus compensated compressor inlet flow function as control parameters. This algorithm allows use of the surge control system in this paper (as shown in Fig. 8), resulting in minimized recycle or blow-off flow. This method reduces the initial cost and simplifies engineering, testing, operation, and maintenance associated with the system when compared to alternative methods. The input signals required to facilitate use of the surge control algorithm on centrifugal compressors are the suction flow differential pressure, suction pressure and discharge pressure. Fig. 8 Proposed supervision schema in compression system Using the fuzzy logic model, it was possible to analyze the deficiencies of the orig- inal surge control algorithm by observing the “real” surge margin calculated from the compressor performance, the objective of an anti-surge controller should not be lim- ited to basic independent machine protection. The anti-surge control performance as an integral part of the machine performance control must be considered. Storing real surge points, applying fuzzy logic control of the recycle valve (variable gain depend- ing on operating region) and compensating for interaction between surges, overload and process control can significantly expand the operating window. This allows oper- ation very close to the actual surge lines (4-8%) under all process conditions. Straight Fuzzy Inf. Eng. (2010) 1: 49-73 61 line surge control, even with variable slope, must make allowance for the poor fit to actual surge points by using a wider margin (15-20%). Interim remedial actions to improve the surge control constants were carried out until an advanced complex control system was installed. An identical steady-state model that was built separately helped to design and test the revised compressor surge control algorithm prior to commissioning on the compressor. In the course of developing fault diagnosis schemes, the use of analytical redun- dancy implies that a mathematical model of the system is used to describe the inherent relationship (or redundancy) contained among the system inputs and outputs which may be used to generate the residuals for fault diagnosis. The resulting approaches are usually referred to as analytical redundancy based fault diagnosis or model based methods [17]. This is the approach we take here; the proposed approach consists of the basic steps residual generation, residual evaluation and fault alarm presentation as shown in Fig. 9. Fig. 9 General scheme of model-based FDI system The evaluation of the residual signals generated by the models is performed us- ing an expert supervisory scheme. The heuristic knowledge of faults and processing experience can be incorporated into the expert system in the form of rules easily, and thus its advantages are the transparency of operation and simple integration of a priori knowledge. Basically, the rule-based expert supervisory system performs two functions. The residual evaluation is a logic decision making process that transforms quanti- tative knowledge (residuals) into qualitative knowledge (fault symptoms). The goal is to decide if and where in the process the fault has occurred, with a minimum rate of erroneous decision (false alarms) that are caused by the existing disturbances and modeling uncertainties. In Fig. 10, the principle of residual evaluation using fuzzy logic consists of a three-step process. Firstly, the residuals have to be fuzzified, then they have to be evaluated by an inference mechanism using IF-THEN rules, and fi- nally they have to be defuzzified to obtain a decision. The mean value of the residual r (t) on a temporal window of p sampling periods T, x (t)isgiven by k 62 Ahmed Hafaifa · Kouider Laroussi · Ferhat Laaouad (2010) Fig. 10 Residual evaluation concept x (t) = r (t− j). (10) k k j=0 The residual derivative x (t) will be estimated on the same temporal window by a least square linear approximation p p p p jr (t− j)− j r (t− j) k k j=0 j=0 j=0 x (t) = . (11) p p p j − j j=0 j=0 The use of mean values over a small temporal window (in the application p = 8) somewhat filters the measurement noise and at the same time allows a quick determi- nation of any change in the residuals. To enhance the diagnostic performance, especially to reduce false alarm, the resid- uals are subjected to a second layer of filtering. Indeed, if we consider the residual r(k) given by [1, 17]: (12) r(k) = y(k)−y( ˆ k), the mean value x (t) of this residual on a temporal window of p sampling is given by x (t) = r ((t− j)T ) (13) k k j=0 with T being the sampling period. Using a least square linear approximation, the change in x (t) is given by: p p p p jr (t− j)− j r (t− j) k k j=0 j=0 j=0 x (t) = . (14) p p p j − j j=0 j=0 Fuzzy Inf. Eng. (2010) 1: 49-73 63 The use of means values, over a small temporal window, filters the measurements noise and allows a quick determination of any change in the residuals. In this paper a symmetric trapezoidal membership functions are used in residual evaluation for the fuzzification, as shown in Fig. 11 with b = a+δ, (15) where a is corresponds to a certain amplitude of the noise, andδ is the variance of the noise. Fig. 11 Membership functions used in residual evaluation For our application, it is more judicious to take b = r for the identification of i imax the faults so that, for a value r (t) of residual i: 0, r (t) ≤ a, r (t)− a u (r (t)) = , r (t) ∈ [a, b ], (16) Positi f i i i b − a 1, r (t) ≥ b. i i In this work, two fuzzy implications, shown in Fig. 12, enable us to deduce indi- cators from faults: • Implication de Brouwer-Gdoel ¨ [20, 23]: ⎛ ⎞ ⎜ ⎪ 1, d ≤ u (r (t))⎟ ⎜ ⎨ ij Positi f i ⎟ ⎜ ⎟ ⎜ ⎟ F(e ) = min . (17) ⎜ ⎪ ⎟ ⎝ ⎠ u (r (t)), no Positi f i i 64 Ahmed Hafaifa · Kouider Laroussi · Ferhat Laaouad (2010) Fig. 12 Fuzzy implications used in residual evaluation • Implication de Goguen [20, 23]: ⎛ ⎧ ⎞ u (r (t)) ⎜ ⎪ Positi f i ⎟ ⎜ ⎪ ⎟ ⎜ ⎟ ⎪ min , 1 , d  0 ⎜ ij ⎟ ⎜ ⎨ ⎟ ⎜ ⎟ F(e ⎜ ij ⎟ . (18) ) = min j ⎜ ⎪ ⎟ ⎜ ⎪ ⎟ i ⎜ ⎟ ⎝ ⎠ 1, no 5. Application Results In this section, we present several experimental results to demonstrate the feasibility of the proposed fuzzy FDI scheme. The proposed fuzzy model-based FDI is experi- mentally investigated in the examined compression system (gas compression station in Algeria SC /Sonatrach). We present in this section the results of implementation of the proposed approach. There are two scenarios of measurements available: in the first situation, the com- pression system is in surge without control, in this case, we run scenarios with con- secutive defects have been introduced in order to evaluate the behavior of residues and their symptoms associated with defects detecting surge phenomenon in our com- pression system for the different variable parameters. The amplitudes of faults were applied obviously chosen to exceed the corresponding limits of detection. The re- sponse of the different types of surge in our compression system, for the different variable parameters with the associate residuals, can be seen in figures 13, 14, 15, 16, 17, 18 and 19. Fuzzy Inf. Eng. (2010) 1: 49-73 65 Fig. 13 Results of the fault detection in compression system with surge: mass flow input Fig. 14 Results of the fault detection in compression system with surge: mass flow output 66 Ahmed Hafaifa · Kouider Laroussi · Ferhat Laaouad (2010) Fig. 15 Results of the fault detection in compression system with surge: pressure input Fig. 16 Results of the fault detection in compression system with surge: pressure output Fuzzy Inf. Eng. (2010) 1: 49-73 67 Fig. 17 Results of the fault detection in compression system with surge: temperature input Fig. 18 Results of the fault detection in compression system with surge: temperature output 68 Ahmed Hafaifa · Kouider Laroussi · Ferhat Laaouad (2010) Fig. 19 Results of the fault detection in compression system with surge: Rotation speed In the second situation, the compression system with control of surge by using fuzzy logic controller, in this case, the fuzzy logic controller attempts to replicate the functionality of the existing nonlinear controller by using collected real data. The response of the compression system with control of surge by using fuzzy FDI, for the different variable parameters with the associate residuals, is shown in figures 20, 21, 22, 23, 24, 25 and 26. In this case, the behavior of our compression system is considered nominal (without surge). There is no value for the residuals, these signals are exactly zero. Fig. 20 Results of the fault detection in compression system by using fuzzy control: mass flow input Fuzzy Inf. Eng. (2010) 1: 49-73 69 Fig. 21 Results of the fault detection in compression system by using fuzzy control: mass flow output Fig. 22 Results of the fault detection in compression system by using fuzzy control: pressure input 70 Ahmed Hafaifa · Kouider Laroussi · Ferhat Laaouad (2010) Fig. 23 Results of the fault detection in compression system by using fuzzy control: pressure output Fig. 24 Results of the fault detection in compression system by using fuzzy control: temperature input Fuzzy Inf. Eng. (2010) 1: 49-73 71 Fig. 25 Results of the fault detection in compression system by using fuzzy control: temperature output Fig. 26 Results of the fault detection in compression system by using fuzzy control: Rotation speed 72 Ahmed Hafaifa · Kouider Laroussi · Ferhat Laaouad (2010) In this work, a new approach to fault diagnosis by using fuzzy fault and detection and isolation has been presented. The significant advantage of the new approach is that it is given unbiased estimates of the parameter variations in a straightforward way and provides good performance in terms of surge detection and isolation and reduced error. In this paper, recent research work on online intelligent fault detection techniques has been presented including the expert systems approach with fuzzy logic approach in control and in supervision. In addition, the main advantages of fuzzy fault and detection and isolation method is to minimise false alarms enhance detectability and isolability and minimise detection time by hardware implementation. 6. Conclusion The main purpose of this paper is to develop robust FDI scheme by using the TS fuzzy model. We have discussed the modeling of the dynamic behavior of centrifugal compression systems via experimental identification to describe surge transients of a centrifugal compressor. The good agreement between fuzzy modeling results and fuzzy supervision schema based on robust FDI can be very well integrated with any conventional control scheme to develop a fault tolerant control scheme. The intro- duced fuzzy faults detection and isolation approach contain various parameters that require tuning when the model is applied to a specific compression system. The ap- plied fuzzy supervision schema give good results that were obtained with the applied control approach, it is observed that probability of missed false alarms in compression system. Fuzzy FDI method defining the surge point over a wide range of changing condi- tions makes it possible to set the control line for optimum surge protection without unnecessary re-cycling. This method automatically compensates for changes in pres- sure rise, mass flow, temperature, and compressor rotor speed. The system utilizes a characterization of compression ratio versus compensated compressor inlet flow func- tion as control parameters. This algorithm allows for use of the surge control system in this paper, resulting in minimized recycle or blow-off flow. This method reduces the initial cost and simplifies engineering, testing, operation, and maintenance asso- ciated with the system when compared to alternative methods. The business benefits of this fuzzy FDI method open, flexible, proactive approach to compression system monitoring and maintenance are not only improved fault di- agnosis performance, but also reusable service assemblies, better scalability, better maintainability, higher availability, reduction in unscheduled maintenance and result- ing reduction in compression system. References 1. Amann P, Perronne J M, Gissinger G L, Frank P M (2001) Identification of fuzzy relational models for fault detection. Control Engineering Practice 9(5): 555-562 2. Corina H J Meuleman (2002) Measurement and unsteady flow modelling of centrifugal compressor surge. Doctoral thesis. Netherlands : University of technology of Eindhoven 3. Evsukoff A, Gentil S (2005) Recurrent neuro-fuzzy system for fault detection and isolation in nuclear reactors. Advanced Engineering Informatics 19(1): 55-66 4. Franciscus P, Willems T (2000) Modeling and bounded feedback stabilization of centrifugal com- pressor surge. Doctoral thesis. Netherlands : University of technology of Eindhoven Fuzzy Inf. Eng. (2010) 1: 49-73 73 5. Gravdahl J T, Willems F, Jager De B, Egeland O (2004) Modeling of surge in free-spool centrifugal compressors: Experimental validation. Journal of Propulsion and Power 20(5): 849-857 6. Gravdahl J T, Egeland O, Vatland S O (2002) Drive torque actuation in active surge control of cen- trifugal compressors. Automatica 38(11): 1881-1893 7. Greitzer E M, Moore F K (1986) A theory of post-stall transients in a axial compressor systems, Part II: application. Journal of Engineering for Gas Turbines and Power 108: 223-239 8. Greitzer E M (1980) Axial compressor stall phenomena. Journal of Fluids Engineering 102: 134-151 9. Greitzer E M (1976) Surge and rotating stall in axial flow compressors, Part I: Theoretical compres- sion system model. Journal of Engineering for Power 98: 190-198 10. Greitzer E M (1976) Surge and rotating stall in axial flow compressors, Part II: Experimental results and comparison with theory. Journal of Engineering for Power 98: 199-217 11. Greitzer E M, Griswold H R (1976) Compressor-diffuser interaction with circumferential flow distor- tion. Journal of Mechanical Engineering Science 18(1): 25-43 12. Gysling D L, Greitzer E M (1995) Dynamic control of rotating stall in axial flow compressors using aeromechanical feedback. ASME Journal of Turbomachinery 117: 307-319 13. Hafaifa A, Laaouad F, Laroussi K (2010) Fuzzy logic approach applied to the surge detection and isolation in centrifugal compressor. Automatic Control and Computer Sciences 44(1): 53-59 14. Hafaifa A, Laaouad F, Guemana M (2009) A new engineering method for fuzzy reliability analysis of surge control in centrifugal compressor. American Journal of Engineering and Applied Sciences 2(4): 676-682 15. Hafaifa A, Laaouad F, Laroussi K (2009) Centrifugal compressor surge detection and isolation with fuzzy logic controller. International Review of Automatic Control (Theory and Applications) - issue of January 2(1): 108-114 16. Hafaifa A, Laaouad F, Bennani A (2008) Model-based component fault detection and isolation in the centrifugal compressor using fuzzy logic approach. Proc. of the 1st Algerian-German International Conference on New Technologies and Their Impact on Society AGICNT 2008, Sl tif Algeria 17. Isermann R (2005) Model-based fault-detection and diagnosis-status and applications. Annual Re- views in Control 29(1): 71-85 18. Karlsson A, Arriagada J, Genrup M (2008) Detection and interactive isolation of faults in steam turbines to support maintenance decisions. Simulation Modelling Practice and Theory 16(10): 1689- 19. Moore F K, Greitzer E M (1986) A theory of post-stall transients in axial compression systems, Part I: Development of equations. ASME Journal of Engineering for Gas Turbines and Power 108(1): 68-76 20. Nanda S (2006) Fuzzy logic and optimization. India: Narosa edition 21. Paduano J D, Greitzer E M, Epstein A H (2001) Compression system stability and active control. Annual Review of Fluid Mechanics 33: 491-517 22. Willems F, Heemels W P M H, Jager De B, Stoorvogel A A (2002) Positive feedback stabilization of centrifugal compressor surge. Automatica, 38(2): 311-318 23. Yager R R, Filev D P (1994) Essentials of fuzzy modeling and control (1 edition). Canada: Wiley http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Fuzzy Information and Engineering Taylor & Francis

Robust Fuzzy Fault Detection and Isolation Approach Applied to Surge in Centrifugal Compressor Modeling and Control

Download PDF
25 pages

Loading next page...
 
/lp/taylor-francis/robust-fuzzy-fault-detection-and-isolation-approach-applied-to-surge-XqPPFYiIdq

References (26)

Publisher
Taylor & Francis
Copyright
© 2010 Taylor and Francis Group, LLC
ISSN
1616-8666
eISSN
1616-8658
DOI
10.1007/s12543-010-0037-6
Publisher site
See Article on Publisher Site

Abstract

Fuzzy Inf. Eng. (2010) 1: 49-73 DOI 10.1007/s12543-010-0037-6 ORIGINAL ARTICLE Robust Fuzzy Fault Detection and Isolation Approach Applied to Surge in Centrifugal Compressor Modeling and Control Ahmed Hafaifa · Kouider Laroussi· Ferhat Laaouad Received: 1 October 2009/ Revised: 30 January 2010/ Accepted: 6 February 2010/ © Springer-Verlag Berlin Heidelberg and Fuzzy Information and Engineering Branch of the Operations Research Society of China 2010 Abstract This work presents the results of applying an advanced fault detection and isolation technique to centrifugal compressor; this advanced technique uses physics models of the centrifugal compressor with a fuzzy modeling and control solution method. The fuzzy fault detection and isolation has become an issue of primary im- portance in modern process engineering automation as it provides the prerequisites for the task of fault detection. In this work, we present an application of this approach in fault detection and isolation of surge in compression system. The ability to detect the surge is essential to improve reliability and security of the gas compressor plants. We describe and illustrate an alternative implementation to the compression systems supervision task using the basic principles of fuzzy fault detection and isolation asso- ciated with fuzzy modeling approach. In this supervision task, the residual generation is obtained from the real input-output data process and the residual evaluation is based on fuzzy logic method. The results of this application are very encouraging with rel- atively low levels of false alarms and obtaining a good limitation of surge in natural gas pipeline compressors. Keywords Compression system· Centrifugal compressor· Fuzzy modeling· Fuzzy control· Fuzzy fault detection and isolation· Surge phenomena· Supervision system 1. Introduction The compression systems are used in a wide variety of applications [2, 4, 9, 21]. These includes turbojet engines used in aerospace propulsion, power generation using industrial gas turbines, turbocharging of internal combustion engines, pressurization of gas and fluids in the process industry, transport of fluids in pipelines and so on. Ahmed Hafaifa () · Kouider Laroussi · Ferhat Laaouad Industrial Automation and Diagnosis Systems Laboratory, Science and Technology Faculty, University of Djelfa, 17000, DZ Algeria email: hafaifa@hotmail.com 50 Ahmed Hafaifa · Kouider Laroussi · Ferhat Laaouad (2010) These manufacturers are greatly interested with any improvement in performance, life and weight reduction without loss of reliability. Therefore, it is worthwhile to carefully estimate the reliability of rotating systems in order to improve the supervi- sion and the control system or eventually modify the design. Reliability analysis of the supervision structure require some information on the model of the compression system. We know it is difficult to obtain the mathematical model for a complicated mechanical structure. The turbo compressor is considered as a complex system where many modeling and controlling efforts have been made [14]. In regard to the complexity and the strong non linearity of the turbo compressor dynamics, and the attempt to find a simple model structure which can capture in some appropriate sense the key of the dynamical properties of the physical plant, we pro- pose to study the application possibilities of the recent supervision approaches and evaluate their contribution in the practical and theoretical fields consequently. Fac- ing to the studied industrial process complexity, we choose to make recourse to fuzzy logic for analysis and treatment of its supervision problem owing to the fact that these technique constitute the only framework in which the types of imperfect knowledge can jointly be treated (uncertainties, inaccuracies,··· )offering suitable tools to char- acterize them. In the particular case of the turbo compressor, these imperfections are interpreted by modelling errors, the neglected dynamics and the parametric vari- ations. This work presents the results of applying an advanced fault detection and isola- tion technique to centrifugal compressor; this advanced technique uses physics mod- els of the centrifugal compressor with a fuzzy modeling and control solution method. The technique automatically finds the best fault scenario to match measured (or test) data. The best fault scenario provides information about parameter deviations (i.e., fault detection) and fault-contributing components (i.e., isolation). The technique is independent of the thresholds used in fault detection as in some other techniques. The technique is effective even under the condition where data are scarce and widely spaced in time. Operational data from the gas compression station of SONATRACH, SC in Algeria. The purpose of the data is to apply the fuzzy model-based fault iden- tification expertise to industrial gas pipeline. The investigation was conducted with extremely limited knowledge of the compression system and their maintenance his- tories. The measured variables, provided in the data set, only include surge, speed, exhaust temperature, flow, and compressor discharge pressure. With these limited compression system data, we modified an existing, generic model for centrifugal compressor and developed the fuzzy method to “hunt” for suspicious fault states. The detection results were confirmed by the method of validation. The detection ac- curacy of this technique can be improved with additional data and knowledge about the centrifugal compressor. This technique can be readily generalized to fault/state detection of other types of centrifugal compressor in all industries. The presented approach is based on the use of the fuzzy model. As was introduced in [23], by applying a Takagi-Sugeno (TS) type fuzzy model with interval param- eters, one is able to approximate the upper and lower boundaries of the domain of functions that result from an uncertain system. The fuzzy model is therefore intended for robust modelling purposes; on the other hand, studies show it can be used in fault Fuzzy Inf. Eng. (2010) 1: 49-73 51 detection as well. The novelty lies in defining of confidence bands over finite sets of input and output measurements in which the effects of unknown process inputs are already included. Moreover, it will be shown that by data pre-processing the fuzzy model parameter-optimization problem will be significantly reduced. By calculating the normalized distance of the system output from the boundary model outputs, a nu- merical fault measure is obtained. The main idea of the proposed approach is to use the fuzzy model in a Fault Detection and Isolation (FDI) system as residual genera- tors, and combine the fuzzy model outputs for the purpose of fault isolation. Due to data pre-processing, the decision stage is robust to the effects of system disturbances. This paper presents a new method for fault diagnosis of a compression system. The method determines performance indices using fuzzy FDI approach. Firstly, we describe the case study of surge in gas compression system in Section 2. Secondly in Section 3, by using fuzzy modeling in FDI for the compression system control, the proposed method can achieve high performance in the surge control of the compres- sion system. In Section 4, this work illustrates an alternative implementation to the compression systems supervision task using the basic principles of model-based FDI associated with the self-tuning of surge measurements with subsequent appropriate corrective actions. Using a combination of fuzzy modeling approach makes it possi- ble to devise a fault-isolation scheme based on the given incidence matrix. After that in Section 5, followed by experimental results that confirm the effectiveness of the proposed approach in the application results section. In its final part the paper gives some conclusions about this application. 2. Gas Compression System The complex models for surge in centrifugal compression systems have been pro- posed by many authors [5, 10, 12, 22]. An essential step in model-based controller design is to understand the physical phenomena in the system and to develop a math- ematical model that describes the dynamics of the relevant phenomena. In this work, the examined compression system is modeled with just three components. The first component is the inlet duct that allows infinitesimally small disturbances at the duct entrance to grow until they reach an appreciable magnitude at the compressor face. The second component is the compressor itself, modeled as an actuator disk, which raises the pressure ratio by doing work on the fluid. The third component is the plenum chamber (or diffuser) downstream, which acts as a large reservoir and re- sponds to fluctuations in mass flow with fluctuations in pressure behind the actuator disk. In this paper, we are considering a compression system consisting of a centrifu- gal compressor, Close Coupled Valve (CCV), compressor duct, plenum volume and a throttle. The throttle can be regarded as a simplified model of a turbine [4, 6, 12]. The gas turbine installation used in our application for studies of compressor surge detection and control is shown in Fig. 1. 52 Ahmed Hafaifa · Kouider Laroussi · Ferhat Laaouad (2010) Fig. 1 Compression system 2.1. Surge in Centrifugal Compressor Centrifugal compressors will surge when forward flow through the compressor can no longer be maintained, due to an increase in pressure across the compressor, and a momentary flow reversal occurs. Once surge occurs, the reversal of flow reduces the discharge pressure or increases the suction pressure, thus allowing forward flow to resume again until the pressure rise again reaches the surge point [10]. Surge is characterized by large amplitude fluctuations of the pressure and by unsteady, but circumferentially uniform, annulus-averaged mass flow. This essentially one dimen- sional instability affects the compression system as a whole and results in a limit cycle oscillation in the compressor map. This surge cycle will continue until some change is made in the process or compressor conditions. Fig. 2 shows a pressure trace for a compressor system, which was initially operated in a steady operating point. By throttling the compressor mass flow, the machine is run into surge. This figure illus- trates the difference between pressure variations before and after surge initiation. A surge controller typically measures a function of pressure rise versus flow. The con- troller operates a surge valve to maintain sufficient forward flow to prevent surge [4, 5, 7, 8, 11]. The optimum flow rate may be calculated from a simple graph of pressure differ- Fuzzy Inf. Eng. (2010) 1: 49-73 53 Fig. 2 Surge mode in centrifugal compressor Fig. 3 Compressors characteristic curves ence against flow, as shown on Fig. 3. The position of the lines is unique to a par- ticular compressor. The operating setpoint is at the minimum flow rate and pressure difference which avoids surge conditions. The application fuzzy logic for anti-surge control provides a fine and reliable control mechanism maintaining the process close to this setpoint. Many papers and texts on anti-surge control maintain that the onset of surge can occur in as little as 50ms [6, 12, 13, 18]. They then conclude that this, and the requirement for very ”tight” tuning, implies that a digital anti-surge controller must have an extremely fast repeat time. Compressor users, however, point out that the 54 Ahmed Hafaifa · Kouider Laroussi · Ferhat Laaouad (2010) blow off or recycle valve driven by the controller is unlikely to open in less than 2 seconds. The process automation anti-surge control fuzzy logic has been proven to successfully meet the above criteria with repeat times of 75 to 100 ms. 2.2. Centrifugal Compressor Model The resulting equations of the dynamics of the compression system in the model used for controller design are in the form: kP ⎪ 01 P = m− k P − P , ⎪ p t p 01 ρ V ⎪ 01 p ⎡ ⎤ ⎪ 4(k−1) ⎢ k ⎥ ⎪ ⎢ ⎥ A Δh ⎨ ⎢ ⎥ 1 ideal ⎢ ⎥ ⎢ ⎥ m = P 1+η (m, N) − P , (1) ⎪ ⎢ 01 i p⎥ ⎣ ⎦ L C T ⎪ c p 01 η m C ΔT ⎪ 1 t tur p,t tur N = − 2r σπN | m | , 2Jπ 2πN where P is the plenum pressure, K is a numerical constant, P is the ambient pres- p 01 sure,ρ is the inlet stagnation density, V is the plenum volume, m is the compressor 01 p mass flow, k is a parameter proportional to throttle opening, A is the area of the t 1 impeller eye (used as reference area), L is the length of compressor and duct, η is c i the isentropic efficiency, N is the spool moment of inertia, Δh is the total specific ideal enthalpy delivered to fluid, c is the specific heat capacity at constant pressure, c is p v the specific heat capacity at constant volume, T is the inlet stagnation temperature and k is the ratio of specific heats k = . Moore and Greitzer model in [19] gives rise to three ordinary differential equa- tions, the first for the non-dimensional total-to-static pressure riseΔp across the com- pression system, the second for the amplitude of mass flow rate fluctuations m, and the third for the non-dimensional, spool moment of inertia. In the following, and based on the work of Moore and Greitzer model we used the two first equations of (1) equivalent to the model of [4]. The linearization of this model given by [2] around a point of operation M (P , m , u , u )give: pc0 c0 t0 b0 ⎡ ⎤ ⎡ ⎤ ⎡ ⎤ ⎡ ⎤ ⎢ ˆ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ P ⎥ ⎢ B −B ⎥ ⎢ P ⎥ ⎢ 0 ⎥ pC pC ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ x = ⎢ ⎥ = ⎢ ⎥ ⎢ ⎥ + ⎢ ⎥ u ˆ . (2) ⎣ ⎦ ⎣ ⎦ ⎣ ⎦ ⎣ ⎦ b 1 1 V m ˆ m − c c B Bm te B With: t= tw ou ` w it is the frequency of HELMHOLTZ defined by the following H H A B equation: w = a , with a = γRT and B = . The parameters B and G is H a m V L G P C U L A t t C defined by the following equations: B = and G = , B it is the parameter of 2w L L A H c C t stability of GREITZER [9]. 3. Fuzzy Modeling The fuzzy modeling, which directly uses fuzzy rules, is the most important applica- tion in fuzzy theory [23]. Using a procedure originated by Mamdani in the late 70s, three steps are taken to create a fuzzy model for the compression system [23]: Fuzzy Inf. Eng. (2010) 1: 49-73 55 • First, fuzzification (using membership functions to graphically describe a situ- ation). • Second, rule evaluation (application of fuzzy rules). • Third, defuzzification (obtaining the crisp results). Step 1 First of all, the different levels of output (throttle opening, the pressure coefficient and the mass flow coefficient) of the compression system are defined by the triangle membership functions for the fuzzy sets. Step 2 The next step is to define the fuzzy rules. The fuzzy rules are merely a series of if-then statements as mentioned above. These statements are usually derived by an expert to achieve optimum results. The actual value belongs to the fuzzy set zero to a degree of 0.75 for “Pressure coefficient” and 0.4 for “Mass flow coefficient”. Hence, since this is an AND operation, the minimum criterion is used, and the fuzzy set approximately zero of the variable “The throttle opening” is 0.4. Step 3 The result of the fuzzy modeling so far is a fuzzy set. To choose an ap- propriate representative value as the final output (crisp values), defuzzification must be done. This can be done in many ways, but the most common method used is the center of gravity of the fuzzy set. Fuzzy models are flexible mathematical structures that, in analogy to nonlinear models, have been recognized as universal function approximators [1, 3, 23]. Fuzzy models use ‘If-Then’ rules and logical connectives to establish relations between the variables defined for the model of the system. For the given example, let the system to model be the relation between surge and the fluctuations in the mass flow coefficient ΔΦ and pressure coefficient ΔΨ. Thus, in fuzzy modeling the fuzzy ‘If-Then’ rules take the form: I f u is surge then y is High. (3) The fuzzy sets in the rules serve as an interface amongst qualitative variables in the model, and the input and output numerical variables. The fuzzy modeling approach has several advantages when compared to other nonlinear modeling techniques; in general, fuzzy models can provide a more transparent representation of the system under study, maintaining a high degree of accuracy. 3.1. Fuzzy TS Models Developing mathematical models for nonlinear systems can be quite challenging. However, TS fuzzy systems are capable of serving as the analytical model for non- linear systems due to its universal approximation property, that is, any desired ap- proximation accuracy can be achieved by increasing the size of the approximation structure and properly defining the parameters of the approximators [20, 23]. A TS fuzzy system can be defined by: 56 Ahmed Hafaifa · Kouider Laroussi · Ferhat Laaouad (2010) g (x)μ (x) i i ⎪ i=1 y = F (x,θ) = , ts ⎪ R ⎪ μ (x) i=1 (4) g (x) = a + a x +···+ a x , ⎪ i i,0 i,1 1 i,n n ⎛ ⎞ ⎛ ⎞ ⎪ n ⎜ ⎟ ⎜ ⎜ x − c ⎟ ⎟ ⎪ 1 ⎜ ⎜ j ⎟ ⎟ ⎜ ⎜ ⎟ ⎟ ⎜ ⎜ ⎟ ⎟ μ (x) = exp ⎜ − ⎜ ⎟ ⎟ , ⎪ i ⎜ ⎝ ⎠ ⎟ ⎪ i ⎝ ⎠ j=1 where y is the output of the fuzzy system, x = [x , x ,··· , x ] holds the n inputs, 1 2 n i = 1, 2,··· , R represent R different rules, and j = 1, 2,··· , n represent n different inputs, the shapes of the membership functions are chosen to be Gaussian, and center- average defuzzification and product are used for the premise and implication in the structure of the fuzzy system. The g (x) are called consequent functions of the fuzzy system, where a are linear parameters. The premise membership functions μ (x) i, j i are assumed to be well defined so that μ (x)  0. The parameters that enter in i=1 i i a nonlinear fashion are c and σ , which are the centers and relative widths of the j j th th membership functions for the j inputs and i rules. The TS fuzzy model consists of representing the base rules as follows: R : If u is A then y = f (u), i = 1, 2,··· , K, (5) i i i where R denotes the i h rule, K is the number of rules, u is the antecedent variable, y is the consequent variable and A is the antecedent fuzzy set of the i h rule. Each rule i hasadifferent function f yielding a different value for the output y . The most i i simple and widely used function is the affine linear form: R : If u is A then y = a u+ b, i = 1, 2,··· , K, (6) i i i where a is a parameter vector and b is a scalar offset. i i 3.2. Fuzzy Models of Compression System The fuzzy logic model is a rule-based system that receives information fed back from the plant’s operating, in this case the normalized fluctuations ofΦ andΨ. These crisp values are fuzzified and processed using the fuzzy knowledge base [1, 3, 20, 23]. The fuzzy output is defuzzified in throttle and the CCV gains in order to control the plants operating conditions. A fuzzy system involves identifying fuzzy inputs and outputs, creating fuzzy membership functions for each, constructing a rule base, and then deciding what action will be carried out. The response of the system is used to model the control system. Increasing either the throttle gainγ or CCV gainγ will stabilize the system with a penalty of pressure T V lost across the plenum. The fluctuations of the mass flow coefficientΔΦ and pressure coefficientΔΨ are normalized before being sent to the fuzzy model as the crisp input by the following [13, 14, 15, 16]: Fuzzy Inf. Eng. (2010) 1: 49-73 57 |Ψ −Ψ | i i+Δt ΔΨ = , (7) max(Ψ,Ψ ) i i+Δt |Φ −Φ | i i+Δt ΔΦ = . (8) max(Φ,Φ ) i i+Δt Samples of the coefficients are taken at regular time-step intervals, Δt = kh where k is a constant and h is the Runge-Kutta time step size. The crisp output from the fuzzy model adjusts both control gains by the following: γ = γ +γΔγ. (9) i+Δt i i i For the case of two inputs and one output, the rule base is constructed by creating a matrix of options and solutions. The matrix has the input variable along the top side. The entries in the matrix are the desired response of the system, the changes in either throttle or CCV gain. The rule base of three rules can be created: 1) If [ΔΨ is Low] or [ΔΦ is Low], then [Δγ and Δγ is Low]; V T 2) If [ΔΨ is Medium] or [ΔΦ is Medium], then [Δγ and Δγ is Medium]; V T 3) If [ΔΨ is High] or [ΔΦ is High], then [Δγ and Δγ is High]. V T The results of two simulations are presented in this section. The first is the compar- ison between the complex model, the linearized model and the fuzzy model suggested with Greitzer parameter B = 1.50 for the masse flow coefficient, and the second sim- ulation is the comparison between the complex model, the linearized model and the fuzzy model suggested with Greitzer parameter B = 0.50 for the pressure coefficient. For both simulations the value of J, the squared amplitude of rotating stall was set to zero, and the throttle gain was set so that the intersection of the throttle line and the compressor characteristic is located on the part of the characteristic that has a positive slope. The response of the system with comparison is shown in Fig. 4 for the mass flow coefficient for B = 0.50, the response of the system with comparison for the pressure coefficient for B = 0.50 is shown in Fig. 5. Both simulations push the design point along the compressor characteristic until it reaches a stable operation point without overshooting a stable equilibrium point. An overshoot of the equilibrium conditions would result in pressure lost across the throttle. 58 Ahmed Hafaifa · Kouider Laroussi · Ferhat Laaouad (2010) Fig. 4 Response of complex model, linearized model and fuzzy model for the mass flow coefficient with B = 0.50 Fig. 5 Response of complex model, linearized model and fuzzy model for the pressure coefficient with B= 0.50 The response of the system with comparison is shown in Fig. 6 for the mass flow coefficient for B = 1.50, the response of the system with comparison for the pressure coefficient for B= 1.50 is shown in Fig. 7. According to the above figures, we can notice that our fuzzy logic model is very Fuzzy Inf. Eng. (2010) 1: 49-73 59 Fig. 6 Response of complex model, linearized model and fuzzy model for the mass flow coefficient with B= 1.50 Fig. 7 Response of complex model, linearized model and fuzzy model for the pressure coefficient with B = 1.50 reliable since its outputs match those of the nonlinear complex model with a very small error in a short time interval for the open loop response, hence the obtained model can be used for the output prediction or for the compressor control. Accord- 60 Ahmed Hafaifa · Kouider Laroussi · Ferhat Laaouad (2010) ing to the obtained results it appears clearly that the characteristics of the system of compression describes by the complex model reproduced perfectly by the fuzzy logic model. 4. Compression System Control Based on Fuzzy FDI Fuzzy FDI method defining the surge point over a wide range of changing conditions makes it possible to set the control line for optimum surge protection without unnec- essary re-cycling. This method automatically compensates for changes in pressure rise, mass flow, temperature, and compressor rotor speed. The system utilizes a char- acterization of compression ratio versus compensated compressor inlet flow function as control parameters. This algorithm allows use of the surge control system in this paper (as shown in Fig. 8), resulting in minimized recycle or blow-off flow. This method reduces the initial cost and simplifies engineering, testing, operation, and maintenance associated with the system when compared to alternative methods. The input signals required to facilitate use of the surge control algorithm on centrifugal compressors are the suction flow differential pressure, suction pressure and discharge pressure. Fig. 8 Proposed supervision schema in compression system Using the fuzzy logic model, it was possible to analyze the deficiencies of the orig- inal surge control algorithm by observing the “real” surge margin calculated from the compressor performance, the objective of an anti-surge controller should not be lim- ited to basic independent machine protection. The anti-surge control performance as an integral part of the machine performance control must be considered. Storing real surge points, applying fuzzy logic control of the recycle valve (variable gain depend- ing on operating region) and compensating for interaction between surges, overload and process control can significantly expand the operating window. This allows oper- ation very close to the actual surge lines (4-8%) under all process conditions. Straight Fuzzy Inf. Eng. (2010) 1: 49-73 61 line surge control, even with variable slope, must make allowance for the poor fit to actual surge points by using a wider margin (15-20%). Interim remedial actions to improve the surge control constants were carried out until an advanced complex control system was installed. An identical steady-state model that was built separately helped to design and test the revised compressor surge control algorithm prior to commissioning on the compressor. In the course of developing fault diagnosis schemes, the use of analytical redun- dancy implies that a mathematical model of the system is used to describe the inherent relationship (or redundancy) contained among the system inputs and outputs which may be used to generate the residuals for fault diagnosis. The resulting approaches are usually referred to as analytical redundancy based fault diagnosis or model based methods [17]. This is the approach we take here; the proposed approach consists of the basic steps residual generation, residual evaluation and fault alarm presentation as shown in Fig. 9. Fig. 9 General scheme of model-based FDI system The evaluation of the residual signals generated by the models is performed us- ing an expert supervisory scheme. The heuristic knowledge of faults and processing experience can be incorporated into the expert system in the form of rules easily, and thus its advantages are the transparency of operation and simple integration of a priori knowledge. Basically, the rule-based expert supervisory system performs two functions. The residual evaluation is a logic decision making process that transforms quanti- tative knowledge (residuals) into qualitative knowledge (fault symptoms). The goal is to decide if and where in the process the fault has occurred, with a minimum rate of erroneous decision (false alarms) that are caused by the existing disturbances and modeling uncertainties. In Fig. 10, the principle of residual evaluation using fuzzy logic consists of a three-step process. Firstly, the residuals have to be fuzzified, then they have to be evaluated by an inference mechanism using IF-THEN rules, and fi- nally they have to be defuzzified to obtain a decision. The mean value of the residual r (t) on a temporal window of p sampling periods T, x (t)isgiven by k 62 Ahmed Hafaifa · Kouider Laroussi · Ferhat Laaouad (2010) Fig. 10 Residual evaluation concept x (t) = r (t− j). (10) k k j=0 The residual derivative x (t) will be estimated on the same temporal window by a least square linear approximation p p p p jr (t− j)− j r (t− j) k k j=0 j=0 j=0 x (t) = . (11) p p p j − j j=0 j=0 The use of mean values over a small temporal window (in the application p = 8) somewhat filters the measurement noise and at the same time allows a quick determi- nation of any change in the residuals. To enhance the diagnostic performance, especially to reduce false alarm, the resid- uals are subjected to a second layer of filtering. Indeed, if we consider the residual r(k) given by [1, 17]: (12) r(k) = y(k)−y( ˆ k), the mean value x (t) of this residual on a temporal window of p sampling is given by x (t) = r ((t− j)T ) (13) k k j=0 with T being the sampling period. Using a least square linear approximation, the change in x (t) is given by: p p p p jr (t− j)− j r (t− j) k k j=0 j=0 j=0 x (t) = . (14) p p p j − j j=0 j=0 Fuzzy Inf. Eng. (2010) 1: 49-73 63 The use of means values, over a small temporal window, filters the measurements noise and allows a quick determination of any change in the residuals. In this paper a symmetric trapezoidal membership functions are used in residual evaluation for the fuzzification, as shown in Fig. 11 with b = a+δ, (15) where a is corresponds to a certain amplitude of the noise, andδ is the variance of the noise. Fig. 11 Membership functions used in residual evaluation For our application, it is more judicious to take b = r for the identification of i imax the faults so that, for a value r (t) of residual i: 0, r (t) ≤ a, r (t)− a u (r (t)) = , r (t) ∈ [a, b ], (16) Positi f i i i b − a 1, r (t) ≥ b. i i In this work, two fuzzy implications, shown in Fig. 12, enable us to deduce indi- cators from faults: • Implication de Brouwer-Gdoel ¨ [20, 23]: ⎛ ⎞ ⎜ ⎪ 1, d ≤ u (r (t))⎟ ⎜ ⎨ ij Positi f i ⎟ ⎜ ⎟ ⎜ ⎟ F(e ) = min . (17) ⎜ ⎪ ⎟ ⎝ ⎠ u (r (t)), no Positi f i i 64 Ahmed Hafaifa · Kouider Laroussi · Ferhat Laaouad (2010) Fig. 12 Fuzzy implications used in residual evaluation • Implication de Goguen [20, 23]: ⎛ ⎧ ⎞ u (r (t)) ⎜ ⎪ Positi f i ⎟ ⎜ ⎪ ⎟ ⎜ ⎟ ⎪ min , 1 , d  0 ⎜ ij ⎟ ⎜ ⎨ ⎟ ⎜ ⎟ F(e ⎜ ij ⎟ . (18) ) = min j ⎜ ⎪ ⎟ ⎜ ⎪ ⎟ i ⎜ ⎟ ⎝ ⎠ 1, no 5. Application Results In this section, we present several experimental results to demonstrate the feasibility of the proposed fuzzy FDI scheme. The proposed fuzzy model-based FDI is experi- mentally investigated in the examined compression system (gas compression station in Algeria SC /Sonatrach). We present in this section the results of implementation of the proposed approach. There are two scenarios of measurements available: in the first situation, the com- pression system is in surge without control, in this case, we run scenarios with con- secutive defects have been introduced in order to evaluate the behavior of residues and their symptoms associated with defects detecting surge phenomenon in our com- pression system for the different variable parameters. The amplitudes of faults were applied obviously chosen to exceed the corresponding limits of detection. The re- sponse of the different types of surge in our compression system, for the different variable parameters with the associate residuals, can be seen in figures 13, 14, 15, 16, 17, 18 and 19. Fuzzy Inf. Eng. (2010) 1: 49-73 65 Fig. 13 Results of the fault detection in compression system with surge: mass flow input Fig. 14 Results of the fault detection in compression system with surge: mass flow output 66 Ahmed Hafaifa · Kouider Laroussi · Ferhat Laaouad (2010) Fig. 15 Results of the fault detection in compression system with surge: pressure input Fig. 16 Results of the fault detection in compression system with surge: pressure output Fuzzy Inf. Eng. (2010) 1: 49-73 67 Fig. 17 Results of the fault detection in compression system with surge: temperature input Fig. 18 Results of the fault detection in compression system with surge: temperature output 68 Ahmed Hafaifa · Kouider Laroussi · Ferhat Laaouad (2010) Fig. 19 Results of the fault detection in compression system with surge: Rotation speed In the second situation, the compression system with control of surge by using fuzzy logic controller, in this case, the fuzzy logic controller attempts to replicate the functionality of the existing nonlinear controller by using collected real data. The response of the compression system with control of surge by using fuzzy FDI, for the different variable parameters with the associate residuals, is shown in figures 20, 21, 22, 23, 24, 25 and 26. In this case, the behavior of our compression system is considered nominal (without surge). There is no value for the residuals, these signals are exactly zero. Fig. 20 Results of the fault detection in compression system by using fuzzy control: mass flow input Fuzzy Inf. Eng. (2010) 1: 49-73 69 Fig. 21 Results of the fault detection in compression system by using fuzzy control: mass flow output Fig. 22 Results of the fault detection in compression system by using fuzzy control: pressure input 70 Ahmed Hafaifa · Kouider Laroussi · Ferhat Laaouad (2010) Fig. 23 Results of the fault detection in compression system by using fuzzy control: pressure output Fig. 24 Results of the fault detection in compression system by using fuzzy control: temperature input Fuzzy Inf. Eng. (2010) 1: 49-73 71 Fig. 25 Results of the fault detection in compression system by using fuzzy control: temperature output Fig. 26 Results of the fault detection in compression system by using fuzzy control: Rotation speed 72 Ahmed Hafaifa · Kouider Laroussi · Ferhat Laaouad (2010) In this work, a new approach to fault diagnosis by using fuzzy fault and detection and isolation has been presented. The significant advantage of the new approach is that it is given unbiased estimates of the parameter variations in a straightforward way and provides good performance in terms of surge detection and isolation and reduced error. In this paper, recent research work on online intelligent fault detection techniques has been presented including the expert systems approach with fuzzy logic approach in control and in supervision. In addition, the main advantages of fuzzy fault and detection and isolation method is to minimise false alarms enhance detectability and isolability and minimise detection time by hardware implementation. 6. Conclusion The main purpose of this paper is to develop robust FDI scheme by using the TS fuzzy model. We have discussed the modeling of the dynamic behavior of centrifugal compression systems via experimental identification to describe surge transients of a centrifugal compressor. The good agreement between fuzzy modeling results and fuzzy supervision schema based on robust FDI can be very well integrated with any conventional control scheme to develop a fault tolerant control scheme. The intro- duced fuzzy faults detection and isolation approach contain various parameters that require tuning when the model is applied to a specific compression system. The ap- plied fuzzy supervision schema give good results that were obtained with the applied control approach, it is observed that probability of missed false alarms in compression system. Fuzzy FDI method defining the surge point over a wide range of changing condi- tions makes it possible to set the control line for optimum surge protection without unnecessary re-cycling. This method automatically compensates for changes in pres- sure rise, mass flow, temperature, and compressor rotor speed. The system utilizes a characterization of compression ratio versus compensated compressor inlet flow func- tion as control parameters. This algorithm allows for use of the surge control system in this paper, resulting in minimized recycle or blow-off flow. This method reduces the initial cost and simplifies engineering, testing, operation, and maintenance asso- ciated with the system when compared to alternative methods. The business benefits of this fuzzy FDI method open, flexible, proactive approach to compression system monitoring and maintenance are not only improved fault di- agnosis performance, but also reusable service assemblies, better scalability, better maintainability, higher availability, reduction in unscheduled maintenance and result- ing reduction in compression system. References 1. Amann P, Perronne J M, Gissinger G L, Frank P M (2001) Identification of fuzzy relational models for fault detection. Control Engineering Practice 9(5): 555-562 2. Corina H J Meuleman (2002) Measurement and unsteady flow modelling of centrifugal compressor surge. Doctoral thesis. Netherlands : University of technology of Eindhoven 3. Evsukoff A, Gentil S (2005) Recurrent neuro-fuzzy system for fault detection and isolation in nuclear reactors. Advanced Engineering Informatics 19(1): 55-66 4. Franciscus P, Willems T (2000) Modeling and bounded feedback stabilization of centrifugal com- pressor surge. Doctoral thesis. Netherlands : University of technology of Eindhoven Fuzzy Inf. Eng. (2010) 1: 49-73 73 5. Gravdahl J T, Willems F, Jager De B, Egeland O (2004) Modeling of surge in free-spool centrifugal compressors: Experimental validation. Journal of Propulsion and Power 20(5): 849-857 6. Gravdahl J T, Egeland O, Vatland S O (2002) Drive torque actuation in active surge control of cen- trifugal compressors. Automatica 38(11): 1881-1893 7. Greitzer E M, Moore F K (1986) A theory of post-stall transients in a axial compressor systems, Part II: application. Journal of Engineering for Gas Turbines and Power 108: 223-239 8. Greitzer E M (1980) Axial compressor stall phenomena. Journal of Fluids Engineering 102: 134-151 9. Greitzer E M (1976) Surge and rotating stall in axial flow compressors, Part I: Theoretical compres- sion system model. Journal of Engineering for Power 98: 190-198 10. Greitzer E M (1976) Surge and rotating stall in axial flow compressors, Part II: Experimental results and comparison with theory. Journal of Engineering for Power 98: 199-217 11. Greitzer E M, Griswold H R (1976) Compressor-diffuser interaction with circumferential flow distor- tion. Journal of Mechanical Engineering Science 18(1): 25-43 12. Gysling D L, Greitzer E M (1995) Dynamic control of rotating stall in axial flow compressors using aeromechanical feedback. ASME Journal of Turbomachinery 117: 307-319 13. Hafaifa A, Laaouad F, Laroussi K (2010) Fuzzy logic approach applied to the surge detection and isolation in centrifugal compressor. Automatic Control and Computer Sciences 44(1): 53-59 14. Hafaifa A, Laaouad F, Guemana M (2009) A new engineering method for fuzzy reliability analysis of surge control in centrifugal compressor. American Journal of Engineering and Applied Sciences 2(4): 676-682 15. Hafaifa A, Laaouad F, Laroussi K (2009) Centrifugal compressor surge detection and isolation with fuzzy logic controller. International Review of Automatic Control (Theory and Applications) - issue of January 2(1): 108-114 16. Hafaifa A, Laaouad F, Bennani A (2008) Model-based component fault detection and isolation in the centrifugal compressor using fuzzy logic approach. Proc. of the 1st Algerian-German International Conference on New Technologies and Their Impact on Society AGICNT 2008, Sl tif Algeria 17. Isermann R (2005) Model-based fault-detection and diagnosis-status and applications. Annual Re- views in Control 29(1): 71-85 18. Karlsson A, Arriagada J, Genrup M (2008) Detection and interactive isolation of faults in steam turbines to support maintenance decisions. Simulation Modelling Practice and Theory 16(10): 1689- 19. Moore F K, Greitzer E M (1986) A theory of post-stall transients in axial compression systems, Part I: Development of equations. ASME Journal of Engineering for Gas Turbines and Power 108(1): 68-76 20. Nanda S (2006) Fuzzy logic and optimization. India: Narosa edition 21. Paduano J D, Greitzer E M, Epstein A H (2001) Compression system stability and active control. Annual Review of Fluid Mechanics 33: 491-517 22. Willems F, Heemels W P M H, Jager De B, Stoorvogel A A (2002) Positive feedback stabilization of centrifugal compressor surge. Automatica, 38(2): 311-318 23. Yager R R, Filev D P (1994) Essentials of fuzzy modeling and control (1 edition). Canada: Wiley

Journal

Fuzzy Information and Engineering – Taylor & Francis

Published: Mar 1, 2010

Keywords: Compression system; Centrifugal compressor; Fuzzy modeling; Fuzzy control; Fuzzy fault detection and isolation; Surge phenomena; Supervision system

There are no references for this article.