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Model-Based Water Wall Fault Detection FBC Boiler Strong Tracking Filter 评分

Fluidized bed combustion (FBC) boilers have received increasing attention in recent decades. Th erosion issue on the water wall is one of the most common and serious faults for FBC boilers. Unlike direct measurement of tube thickness used by ultrasonic methods, the wastage of water wall is reconside
Mathematical Problems in Engineering Dynamics of thermal power P [MWI Measurement residual dP(t) 1 dt IPC(t)-P(t) he(zk) Kalma where the combustion rate in bed QB [kg/s] is QB(t) (WC(t)/tc(Co(t)/C1)and the combustion power Pc [Mw] Pc(t)=10 [HcQB(t)+ Hv vQc(t)]. Here, other deta Kk=PKHK(HKPKHK+RK (12) variable nomenclatures and fine-tuned model parameter Updated state valucs have becn given in [14]. In this Fbc process, the manipulated inputs u are fuel feed Qc [kg/s], primary air flow Zk zk kkp (13) F,[Nm/s], and secondary air flow F2 [Nm/s]; the controlled variables are power P, bed temperature Tg, and freeboard dated covariance oxygen content CE; freeboard temperature T is also a measurable output in addition to the 3 controlled variables PK=(I-KkHkPk (14) Hereby a canonical nonlinear model can be established from (1)-(6) where the superscripts-and represent the values before and after measurement correction, respectively. Fk and Hk are 文=f(x,u) the state transition and observation matrices by linearizing fe a me step y=h(x) However, in most cases, especially for industrial fault diagnostics, the EKF has the following flaws where x= WC CB CF TB Te Pl,u=[Qc FI F2l, and y=ITB P TE CEI (i) poor robustness against model mismatches (il)sensitivity to the statistics of the initial states and 3. Strong Tracking Filt er base noise; State estimation (iii) weak tracking ability to the suddenly changing states 3. 1. Extension and Discretization. If soot formation or erosion All these drawbacks will be more prominent especially occurs in water wall tube, the corresponding heat transfer when filter approaches steady, as shown in the next subsec coefficient will change due to variation ofthermal conduction tion. The essential reason accounting for the phenomenon resistance. However, it is impossible to obtain the heat is that the optimal Kalman gain is actually calculated by transfer coefficient hB by measurement. We can estimate the open-loop method in spite of updating process in state variation of hb by using methods based on joint state and correction. According to the original paper [10] regarding parameter estimation. Considering the influence of noise, linear filtering, the predicted covariance and Kalman gain and assuming hB as an extended statc, the augmented model both depend on the model and initial parameter settings of can be discretized as Po, QK, and Rk. The Kalman gain Kk will approach zero after Z(K+1)-fe((k), u(k))+wk long-time steadiness and then EkF will lose tracking ability when process uncertainty occurs (8) y(k+1)=h2(z(k+1)+vk+1 For this reason, Zhou and Frank proposed a strong tracking filter(STF)in [12]. By introducing a diagonal matrix where z(k)= [x() hB(k) is the augmented state by ak to(10) assuming hB(k 1)=hB(k). Thereby, functions fe and h can be derived from(7)by Euler methods. Wk and vk are the AkFk-IPt-FK 1k-17k-1, (15) process and observation noises which are both assumed to be zero mean multivariate Gaussian noises with covariances Qk the Kalman gain can be adjusted online to maintain the and ri respectively strong tracking ability of filters. The suboptimal fading factors h can be obtained recursively by solving the following q 3.2. Basic Principals of STF. It is well known that the extended Kalman filter(eKF) can be used [15] for the joint estimation E of the systems described by (8), which can be summarized as min, (16) the following formulas Predicted state. k+17+1+j 0;j=1,2, =f2(动-1,uk-1) (9) The second equation of (16)is named orthogonality principle, whose physical meaning is that the residual error series Predicted covariance. hould be made mutually orthogonal at each step, so that the rich information in the residual error series could be +Qk-1 (10 extracted For deduction details, see [12 4 Mathematical Problems in Engineering 160 0.1 0 0500100015002000250030003500400045005000 0500100015002000250030003500400045005000 (a) Fuel inventory [kgl (b)Bed O2 content[Nm/Nm] 0.07 1050 0.065 1000 0.06 950 0.055 900 0.045 800 0500100015002000250030003500400045005000 0.0450010001500200025003000350040004505000 (c) Bed temperature [KI (d)Freeboard O, content(Nm/Nm] 950 945 25.5 940 935 24.5 925 23.5 920 915 22.5 0500100015002000250030003500400045005000 500100015002000250030003500400045005000 STE STE Measurement EKF Measurement EKF (e) Freeboard temperature [K] (f)Thermal power [MWI FIGURE 2: Simulation comparison of estimated states Mathematical Problems in Engineering Soot formation hp2 ∑[(k-)-n、() Actuator FBC plant ensOT d(k)=%21(k) (K Reference (18) Multivariable where N is the preselected data window and d is named detection parameter. When the boiler operates well, d is close to zero. As soon as the fault occurs d will be soarin sensitively. When a threshold Po is defined, the strategy of fault detection is thus, obtained d (k)>Bo (19) Fault detection Fault diagnosis where Bo can be selected by operating experience. With smaller Bo, smaller faults can be detected, but more false alarms occur On the other hand, with larger Bo, only relative FIGURE 3: The structure ot closed-loop fault detection and diagnosis. larger fault can be detected, and missing alarms will increas 3.3. Open-Loop Simulation and Comparison. In this part 4.2. Closed-Loop Structure of Fault Diagnosis. In [16] an open-loop simulation on FBC plant (7)was conducted the authors proposed a multivariable coordinated control without joint estimation. In the simulation, EKF and sTE method of FBC boiler based on LSSVM-GPC, which can shared the same set of filter parameters with initial states control output power and bed temperature well by regulating deviating from the actual value. The simulation results are fucl fccd and primary air flow. Hcrc, a PI controller was shown in Figure 2. In simulating process, the input variable applied in the secondary air flow-freeboard oxygen content (fuel feed Qc) increased by 25 at t =1000 s; the state loop. Based on the above discussion, a closed-loop fault variable(fuel inventory WC) dropped suddenly at t-2000 s detection and diagnosis strategy was developed under the In addition there is a mutation in hcat transfer coefficient h control framework, as shown in Figure 3, where the stron tracking filter was used to estimate state variables and heat at t=3500 s As shown in Figure 2, the adjective "strong"in stF transfer coefficient dually based on(8) implies (i) faster rate of convergence in the presence of initia error(see Figure 2(a)),(ii)stronger tracking ability to the 4.3. Numerical Simulation. The simulation time is 14000s A abrupt changing states regardless of dynamic or stationary load-up command was given with setpoints of P and TB rising fashion, and (iii) better robustness to modeling error (figures to 30 MW and 850 C, respectively, while the setpoint of c 2(c), 2(d), and 2(e), titles: freeboard"and temperature) was kept constant. Suppose soot was deposited gradually in water wall at 4. fdD of water wall t 2000 s and then was cleaned up by soot blower at t=7000 s. After 1000 seconds, tube erosion of water wall 4.1. Strategy of Fault Detection. Once the erosion or soot occurred due to severe attrition. Let Ak= ngI,; that is, the formation occurs, it will grow more and more serious. hence Stf based on multiple fading factors deteriorates to a single it is necessary to detect the fault in time. assume the fault is a fading factor which also has good tracking ability. The closed drift-type process. While the boiler is running at normal state, loop simulation results were shown in Figures 4-6 the heat transfer parameter is It can be scen from Figure 4 that StF can track all the state variables with almost no errors under the condition h()~N(h23o), (17) of joint estimation while ekf is more sensitive to model mismatch(see Figures 4(a) and 4(b)). Figure 5(a) shows the where hg is the normal operating value and oois overwhelming superiority of STF in tracking time-varying reasonable variation which is acceptable for engineering. heat transfer coefficient with unknown changing laws while modified Bayes algorithm is adopted for fault detection the ekf can be used to estimate constant parameters only Define Figure 5(b) shows that the fading factor ak can be increased rapidly once model mismatch happens. Thus the Kalman gain can be adjusted chich accounts for the sti p1(k)=N∑h(k-) ng tracking ability essentially. As shown in Figure 6, the detection parameter d N(Y)7% hypersensitive to water wall fault, which grows exponentially ∑(--h once fault happens. The incipient fault can be detected at an early stage. For example, the soot formation fault is detected at Mathematical Problems in Engineering 800 0.055 700 0.05 00 0.045 0.04 2500 0.035 400 0.03 300 0.025 0.02 200 2000400060008000100001200014000 2000400060008000100001200014000 (a) Fuel inventory [kgl (b)Bed O, content[Nm/NmI 1250 0.03 1150 l00 0.02 1050 0.01 1000 0.01 2000400060008000100001200014000 02000400060008000100001200014000 (c) Bed temperature [K] (d)Freeboard O2 content[Nm/Nm 1200 1150 1050 1000 950 02000400060008000100001200014000 200040006008000100001200014000 State STF Measurement EKF Measurement (e) Freeboard temperature [K (f)Thermal power [MWI FIGURE 4: States estimation of closed-loop simulation Mathematical Problems in Engineering 240 220 Tube attrit 200 180- Soot deposition Soot blo 020004000600080001000012000140000 2000400060008000100001200014000 Actual STE (a)Heat transfer coefficient estimation [W/(m K) (b)Fading factor figure 5: Heat transfer coefficient estimation diagnosis and fault-tolerant control by incorporating other common faults, such as sensor and actuator faults Conflict of Interests Threshold βo te authors declare that there is no conflict of interests garding the publication of this paper Acknowledgment This work has been supported by the National Natural Science foundation of china (nos. 51176086 and 51076071) 1 References 02000400060008000100001200014000 t(s) [1] L F. de Diego, M. de Las obras-Loscertales, A Rufas, F. Garcia Labiano, and P Gayan, Pollutant emissions in a bubbling flu FIGURE G: A semilog graph of detection parameter d idized bed combustor working in oxy-fuel operating conditions effect of flue gas recirculation, Applied Energy, vol 102, pp 860 867,2013 [2]R Leimbach,"Intelligent control of FBC boilers, POWER, vol t=5493 s with estimated fault amplitude,-19.9. The erosion 156,Pp.48-51,2012 fault is detected at t=10006 s with estimated fault amplitude, [3 J. Choi, C. Yi, S. Jo,H. Ryu, and Y. Park, "Simulation of a 19.8(see Figure 5(a). The estimation accuracy of the fault bubbling fluidized bed process for capturing CO, from flue gas, amplitude is 66.4%and 99.3%, respectively. It is possiblc to Korean Journal of Chemical Enginecring, pp. 1-7, 2013 detect a fault earlier if we select a lower threshold but the rate 4]J. Stringer and J. Stallings, Materials issues in circulating of false alarm will correspondingly increase fluidized-bed combustors, in Proceedings of the 11th Interna tional Conference on Fluidized Bed Combustion, vol. 2, Pp. 589 608, ASME, New York, NY, USA, April 1991 5. Conclusion and future work [5]N. G. Solomon, Erosion-resistant coatings for fluidized bed boilers, Materials Performance, voL 37, no 2, pp 38-43, 1998 Because the security and reliability of fbc boiler are becom [6] T.W. Kim, J.-H. Choi,D W Shun et al. ,Wastage rate of water walls in a commercial circulating fluidized bed combustor, The ng more and more important, and the erosion is one of the most common faults of fbc boiler, it is urgent to investigate Canadian Journal of Chemical Engineering, vol. 84, no. 6, Pp 680-687,2006 further the erosion fault of FBC. The Stf is adopted for [7 B.Q. Wang and K Luer, The relative erosivity of limestone, oint estimation due to the virtue of strong robustness against dolomite and coal samples from an operating boiler,Wear, vol model mismatch and strong tracking of drifting states, as well 215,no.12,pp.180-190,1998 as jumping states even when the filter is stable. according to the estimated heat transfer coefficient the soot formation [8] Z. Nawaz, T. Xiaoping, X. Wei, and F. Wei, Attrition behavior of fine particles in a fluidized bed with bimodal particles: influence and erosion can be detected based on the modified Bayes of particle density and size ratio, Korean Journal of chemical algorithm. At last, the simulation results demonstrate that the Engineering, vol 27, no 5, pp 1606-1612, 2010 approach is feasible and effective. The line of research will [9]T-W.Kim, .-H. Choi, D.W.Shun, S.-SKim,SD.Kim,and lead to the future work in comprehensive fault detection and Grace,Wear of water walls in a commercial circulating Mathematical Problems in Engineering fluidized bcd combustor with two gas exits, Powder Technology, vol.178,no.3,Pp.13-150,2007 [10]R E Kalman, A new approach to linear filtering and prediction problems, Journal of Basic Engineering, vol. 82, pp 35-45. 1960 ll] L Ljung, Asymptotic behavior of the extended Kalman filter as a parameter estimator for linear systems, IEEE Transactions on Automatic Control, vol 24, no 1, pp 36-50, 1979 [12] D. H. Zhou and P. M. Frank, Strong tracking filtering nonlinear time-varying stochastic systems with coloured noise application to parameter estimation and empirical robustness analysis, International Journal of Control, vol. 65, nO 2, pp 295 307,1996 [13] E. Ikonen and U. Kortela, Dynamic model for a bubbling fluidized bed coal combustor, Control Engineering Practice, vol 2,no.6,Pp.1001-1006,1994 [14] E. Ikonen and K. Najim, Advanced Process Identification and Control, Marcel Dekker, New York, NY, USA, 2002. [15] A Yoo, T C. Lee, and D R Yang, Experimental simultaneous state and parameter identification of a pH neutralization pro cess based on an Extended Kalman Filter, Korean journal o Chemical Engineering, vol. 21, no 4, Pp. 753-760, 2004 [16 L Sun, L Pan, and Shen, A multivariable coordinated cont method of Fbc boiler based on LSSVM-GPC, Journal of Southeast University, vol 2, Pp 312- 316, 2013 dvances in Advances in Journal of Operations Research Decision Sciences Applied Mathematics Algebra Probabil ty and statistics The scientific temational Journal cf World Journal Differential Equations Hindawi Submit your manuscripts at http://v hindawi. com Internati Advances in Combinatorics Mathermatical Physics Jou Mathematica Problems Discrete Dynam cs in Complex Analysis Mathematics in Engineering pplied Analysis Nature and Society International u Mathematics and Mathematical Sciences Journal of unction spaces Stochastic Analysis Optimization

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