Ash fouling monitoring and soot-blow optimization for reheater in thermal power plant

Applied Thermal Engineering 149 (2019) 62–72

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Applied Thermal Engineering journal homepage: www.elsevier.com/locate/apthermeng

Research Paper

Ash fouling monitoring and soot-blow optimization for reheater in thermal power plant

T

S. Anitha Kumaria, , S. Srinivasanb ⁎

a b

Dept. of Biomedical Engineering, Saveetha School of Engineering, Tamil Nadu, India Dept. of Instrumentation Engineering, M.I.T, Anna University, Tamil Nadu, India

HIGHLIGHTS

cleanliness factor estimated using nonlinear regression model. • Reheater predictors of the nonlinear model identified by rank aggregation. • Optimal optimization strategy for reheater is proposed. • Soot-blow • The methodology has been validated using real time data. ARTICLE INFO

ABSTRACT

Keywords: Ash fouling Cleanliness factor Soot-blow optimization Regression

The paper investigates a comprehensive approach for ash fouling monitoring and an optimized soot-blow mechanism for a thermal power plant reheater. A dynamic nonlinear regression model is designed to monitor the Cleanliness Factor (CF) of reheater and thereby an optimized soot-blow strategy is proposed to determine the critical CF and the duration of soot-blow cycle. The result in this case-study shows that steam consumed per sootblow cycle is reduced and also the amount of fuel used per day is saved by adopting the proposed soot-blow strategy. The proposed method can be implemented as guidance for soot-blow operation in thermal power plants without any need for additional hardware and with a minimal computation.

1. Introduction In coal fired power plants, deposition of ash particles produced during solid fuel combustion lead to drift in process dynamics and it is an undesired phenomenon which causes loss of availability and energy efficiency. To control ash fouling at the heat transfer tubes, sootblowers are operated on a time based schedule which may result in over-blowing in many cases. However, some power plants have replaced time based soot blowing with criteria based methods which includes activation of soot-blow on a predefined cleanliness level. Prediction of fouling with Cleanliness Factor (CF) as a clean measure is greatly influenced by change in dynamics of the operational parameters. In recent years, machine learning regression models are more promising for complicated problem due to its ability in learning the information directly from data than relying on predetermined equation. Nonlinear regression models accommodate wide range of operating conditions and hence estimations using such models are considered to

⁎

be more robust when compared with linear models, especially outside the range of observed data (i.e. extrapolation). In addition nonlinear features such as non-normality, asymmetric cycles, bimodality, nonlinearity between lagged variables and heteroscedasticity can be well described by nonlinear models. The nonlinear models can be either parametric or nonparametric. In parametric approach, the input-output relation for static or dynamic systems is expressed by algebraic or differential equations respectively. The specific form of these parametric models is usually postulated a priori but the selection of structural parameters like degree/order of equations are guided by the data. The advantage of parametric model is that it is parsimonious as it contains limited number of unknown parameters that may be a constant or time-varying based on whether the model is stationary or nonstationary. Nevertheless, these models cannot track process conditions that change abruptly [13]. In nonparametric approach, the input-output relation is represented either analytically in integral equation form where the unknown quantities may be nonlinear functions or input-output mapping

Corresponding author. E-mail address: [email protected] (S. Anitha Kumari).

https://doi.org/10.1016/j.applthermaleng.2018.12.031 Received 24 July 2018; Received in revised form 3 November 2018; Accepted 4 December 2018 Available online 06 December 2018 1359-4311/ © 2018 Elsevier Ltd. All rights reserved.

Applied Thermal Engineering 149 (2019) 62–72

S. Anitha Kumari, S. Srinivasan

Nomenclature

k(Xte) Autocovariance of test point k(X) Autocovariance of training input k(Xtr , Xte) Covariance between training input and a test point Li ith ordered list M Mass of the fluid m Mass flow rate N Number of sample data points nb Number of past inputs of model na Number of past outputs of model nk Number of pure input delay Rf Thermal resistance rLi Rank of independent variable list r Rank of ordered variable list T Temperature of fluid U Overall heat transfer coefficient V( ) Loss function W( ) Weighting matrix Weight associated with each ordered list wi X Predictors of inferential model Xr, Xs Support vectors Gaussian noise { , W1, …Wp, 2} Hyperparameters of Gaussian process , , Model Parameters , Lagrangian multipliers n n c, , Support vector regression model parameters Slack variables representing upper and lower constraint on i, i dependent variable (X) Nonlinear mapping function of inputs Ω Ordered list

Abbreviation CF GPR DEKF MT NLARX NLC PLS-VIP RF RFG RH RLF RMSE SVR SH UVE

Cleanliness Factor Gaussian Process Regression Dual Extended Kalman Filter Metal Temperature Nonlinear Auto Regressive with eXogenous input Neyveli Lignite Corporation Partial Least Square-Variable Importance in Projection Random Forest Random Frog Reheater Relief Root Mean Square Error Support Vector Machine Superheater Uninformative Variable Elimination

Symbols A c D d E(t) f h

Heat transfer surface area Specific heat capacity Kendall’s tau distance Distance measure between ordered list and ith ordered list Error between model output and measured output Nonlinear function relating input and output Convective heat transfer coefficient

combinations (e.g. look-up tables). Nonparametric models are easy to postulate and provide flexibility in approximating nonlinear systems with minimum assumptions. They also follow parsimony. However, it is not recommended to time series with random excitations and when corrupted with significant measurement noise. In view of the above, considering the fact that fouling being complex phenomena, a comprehensive discussion about the nonparametric approaches for CF modelling of reheater is presented. Regression models based on neural networks have been successfully utilized by many researchers for fouling detection. Mohanraj et al. [1] have reviewed the application of artificial neural networks to estimate heat transfer coefficient, fouling factor and friction factor. It has been suggested that neural networks provide a flexible approach in simulating the experimental operating condition. Radhakrishnan et al. [2] have developed a recurrent neural model to predict shell and tube outlet temperatures of crude preheat train, from which the overall heat transfer coefficient is determined by log mean temperature difference approach. The developed neural network model provided a coefficient of determination, R2 equal to 0.98 and Root Mean Square Error (RMSE) equal to 1.83% and 0.93% respectively for tube and shell side temperatures. Mohanty and Singru [3] have modelled shell and tube heat exchanger using wavelet neural network, considering various performance parameters such as shell and tube temperature differences and CF. The closeness of predicted output with that of experimental output is statistically analysed using correct directional change and coefficient of determination. Pena [5] has proposed a probabilistic model based on artificial neural network and adaptive neuro-fuzzy inference system to predict the effectiveness of soot-blow by considering unit load, current relative cleanliness, cleanliness after shedding event as inputs. Degereji et al. [6] have proposed a deposition model to predict slag deposits based on viscosity, static contact angle and surface energy.

Collection of historical data from plant database

Data preprocessing

Model structure and regressor selection

Model parameter estimation

Model validation

No

Model Acceptable

Yes

Fig. 1. Flow chart of inferential modeling procedure.

63

End

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S. Anitha Kumari, S. Srinivasan

The procedure for regression modelling based on measured plant data is presented in Fig. 1. The raw data obtained from database may have been corrupted due to malfunctions in sensors or data acquisition systems. Therefore, the data should be preprocessed in order to improve model quality. It includes de-noising, outlier detection and missing value replacement. The next step is selection of model structure and regressor. Model structure is a set of candidate models among which the model is searched and it is strongly influenced by the purpose of the model. If the process works close to a steady state condition and the process model is applied to classical control strategy, then a linear model is sufficient and in all other cases a nonlinear model can be the best choice to model industrial systems [12]. In general, various machine learning methods such as artificial neural network, neuro-fuzzy systems and statistical learning methods such as Support Vector Regression (SVR) and Gaussian Process Regression (GPR) are available for nonlinear model building. Selection of independent variables and their regressors is closely connected with the problem and selection of model structure. A starting list of influential variables and their regressors can be hypothesized by using expert suggestions and process knowledge. A subset of the relevant model inputs from the initial list can be extracted using methods such as correlation analysis, Mallows’ statistics, Lipschitz quotients, etc. The next step is estimation of model parameters using the measured data by appropriate numerical procedure. In the last step the model is validated and thereby ascertaining that the model adequately fits for the system. The criteria used for model validation generally depend on model residual properties and the data used for model validation should be different from those used for model identification. Ash removal process in coal fired power plants needs an optimization in steam consumption. Soot-blow optimization is formulated to maximize the net benefit of soot-blow (difference between soot blowing

benefits and soot blowing losses) [4]. Statistical fitting of fouling factor for assessing the evolution of fouling in superheater is developed and thereby soot-blow is optimized [7]. Soot-blow optimization strategies proposed [8] to maximize the net soot blowing benefit by soot-blow cycle and time length optimization. Soot-blow optimization model has been developed [9] using a combination of thermodynamic and neural network model to relate boiler cleaning action. In general, soot-blow optimization system determines the cost of steam, cleanliness of heat transfer surfaces and optimum soot blowing interval. Nevertheless, different areas of boiler may accumulate ash deposits at various rates and require separate levels of cleanliness and different amounts of cleaning. Hence, a judicious soot-blow optimization routine in specific to each boiler heating element is necessary. 2. Case study The boiler considered in the case study is a 210 MW lignite-fired power plant boiler available at thermal power plant extension-II, Neyveli lignite corporation (NLC), Neyveli, Tamil Nadu, India. The schematic diagram of the boiler is shown in Fig. 2. The boiler is a drum type with nominal live steam rating of 192 kg/s (540 °C, 178 bar). It is a tangential wall-fired unit with natural circulation design and comprises of three stages of Superheater (SH) and two stages of Reheater (RH). The net calorific value of lignite varies between 9205 and 9832 kJ/kg and hence to run the unit in full load, approximately 190–215 tonnes of lignite have to be burned per hour. The boiler soot blowing system available at NLC is shown in Fig. 3. The boiler is equipped with 24 IK−4 M type soot-blowers (cleaning coverage up to 5.5 m) with three pairs of blowers in each tier comprising of three on the right and three on the left side. The soot-blow steam is supplied from the SH2 stage at a temperature of approximately

Flue gas path

ECON 372˚C

ECON 390˚C

293˚C

-1.28 mbar

340˚C

-1.28 mbar

415˚C

-1.23 mbar

443˚C

-1.05 mbar

546˚C

-0.98 mbar

631˚C

-0.96 mbar

743 ˚C

-1.02 mbar

RH1 446˚C

SH2 568˚C

RH2

674˚C

SH3 790˚C 925˚C

SH1

865˚C

FURNACE -1 mbar

Fig. 2. Pulverized lignite fired boiler at Neyveli power plant. 64

Applied Thermal Engineering 149 (2019) 62–72

S. Anitha Kumari, S. Srinivasan

Steam from SH banks

R I G H T

L E F T C O L U M N

C O L U M N

Fig. 3. Soot blowing system.

440 °C and it is depressurised to 24 bar before letting into the blowers. Each blower is operated for 5 min with a total time of 60 min to complete one cycle. The total steam consumed per operation is approximately 750 kg.

ij (t)

dt

2

h

2 ij

2

c

1

Th,ij 1 (t)

1+

ij h

2

1

Th,ij (t) +

ij

2

h

Tc,i

1j (t)

Tc,ij (t)

ij

= 1 +

h

2 ij

+

dTc,ij (t)

ij

= 1

c

Tc,i

1j (t)

1+

ij

2

c

1

Tc,ij (t) +

ij

2

c

(2)

The model parameters α, β, τh, τc are given by ij (t)

= ,

m h Uij (t) mh (t)U h,

,

c

; h (t) =

m c Uij (t) m hmh ; (t) = ; c (t) = c c mh (t) ij m c (t)U m c (t)

U(t) = U

(mh (t)m c (t)) y (m hy (t) + m cy (t)) (mh mc ) y

(mhy + mc y )

(4)

where the convective heat transfer coefficient of flue gas and steam is denoted by hh and hc (W/m2 K) respectively and the fouling factor is denoted by Rf (W/m2 K) which is equal to zero for clean heat exchanger. The change in U with effect of fouling is indirectly determined by dual extended Kalman filter based parameter (α and β) estimation which is considered to be more efficient than joint extended Kalman filter [11]. The basic framework for Dual Extended Kalman Filter (DEKF) proposed by Wan & Nelson [14] involves parallel estimation of states and parameters by simultaneously updating the state (T) and parameter ( ). The recursive process of DEKF based state and parameter is given in Appendix A.

Th,ij 1 (t)

Th,ij (t)

and

A cUij (t) Mh ; (t) = ; c (t) mh (t) ij m c (t)cc

1 1 1 1 1 R = = = + + f UA Uh Ah Uc A c hh Ah hcA c Ah (1)

1

; h (t) =

where A is the heat transfer surface area (m2), U - overall heat transfer coefficient (W/m2K), M - mass of the fluid, m -mass flow rate (kg/s) and c is specific heat (J/kg/K). Subscript h and c represent the flue gas and steam section with i and j indicating the position of a section where i = 1,…, n and j = 1,…, s. The clean heat transfer coefficient is obtained by theoretical calculations using Eq. (4). The overall heat transfer coefficient is defined by

CF is defined as the ratio of fouled heat transfer coefficient to that of clean heat transfer coefficient. It ranges between 0 and 1, with 1 representing a clean condition. To calculate CF, the fouled heat transfer coefficient is indirectly estimated through the parameters α and β of the model expressed in Eqs. (1) and (2) [15].

dt

Ah Uij (t) mh (t)ch

Mc = m c (t)

3. Determination of CF using dual extended Kalman filter

dTh,ij (t)

=

(3)

are obtained from

4. Rank aggregation In order to develop an accurate and simplified model for monitoring 65

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S. Anitha Kumari, S. Srinivasan

the CF of reheater, it is necessary to select appropriate variables for training. However, it is difficult to determine the correlation intensity between the predictors or independent variable and the dependent variable quantitatively. The method for variable ranking either fall under model-free or model based approach. Model-free variable ranking approaches are based on univariate statistical approaches such as Wilcoxon rank-sum test, Relief (RLF), t-test, etc. Model based variable ranking approaches may be either model-fitting or model-prediction approach. Partial least squares weights, partial least squares loadings, Variable Importance in Projection (VIP) and selectivity ratio are the most commonly used model-fitting approaches. Model-prediction approach of variable ranking depends on the prediction performance of the model by means of cross validation, bootstrap etc. subwindow permutation analysis, Uninformative Variable Elimination (UVE), Random Frog (RFG), Random Forest (RF) comes under modelprediction approach. This multiple methods present a different ranking list. Hence to address this issue, a strategy that combines ranking results of all methods called rank aggregation was introduced [10]. Rank aggregation merges the individual ranking list into single list which reflects the importance of overall population. It is performed using Genetic Algorithm (GA). The objective function of the optimization problem which is given by

5. Nonlinear auto regressive with exogenous input model The Nonlinear Auto Regressive with eXogenous input (NLARX) model structure is defined as [16],

y(t) = f[y(t 1), …, y(t na), X(t nk), …, X(t nk

wi d( , L i) i= 1

V( ) =

Drbg bg L i

1 N

N

ET (t, ) W ( )E(t, )

(9)

t=1

where, N is the number of data samples, E(t, ) is the error vector at a given time t while parameterized by parameter vector θ, W ( ) is the weighting matrix. 6. Kernel based regression

(5)

Kernel regression is a non-parametric technique which predicts continuous dependent variable from limited set of data points by convolving each observational data point location with a kernel function. SVR and GPR are the two widely used regression models and it is used for predicting CF.

where represents the ordered list of length |L i| with L i representing the ith ordered list, wi is the weight associated with each list L i and d is the distance. The optimization problem determines which minimizes the total distance between and L i . Kendall’s tau distance defined by Eq. (6) is used as a distant measure to determine the distance between ordered lists.

D ( , L i) =

(8)

where na, nb represent the number of past outputs and inputs of the model, nk represent input delay. E(t) represent the error between the model output and measured output. The nonlinear function, f is represented by the nonlinearity estimators such as wavelet network, sigmoid network, multilayered neural network, tree partition. The model parameters are estimated by minimizing the loss function, V( ) as represented by Eq. (9). This loss function is a weighted sum of error, E(t) .

m

( )=

nb + 1)] + E(t)

6.1. Support vector regression

(6)

SVR is a machine learning tool for regression, first proposed by Vapnik [18]. It estimates the relationship between the predictors and the dependent variable by using kernel functions. If the set of data is n represented by {(Xi, yi), i= 1, …, N}, X then formulation of SVR is to find the nonlinear function f(X) which has the most - deviation from the training outputs and is less sensitive to errors in measurement or nonstationarity of the inputs. The function represented by Eq. (10) need to be estimated such that the points contained within the -tube are not penalized, f(X) y .

where Li Li Li Li 0 if r (b) < r (g), r (b) < r (g)or r (b) > r (g), r (b) > r (g) Dqbg = 1 if r (b) > r (g), r Li (b) < r Li (g)or r (b) < r (g), r Li (b) > r L i (g) q if r (b) = r (g ) = v+ 1or r Li (b) = r Li (g) = v+ 1

(7) where, r and r L i represents the rank of ordered list and the independent list respectively. q [0 1] is the parameter that needs to be initialised for Kendall’s tau. If two elements in the ordered list, say b and g have the same ordering in both list then is a good scenario and 0 penalty is incurred. If the element b precedes g in the first list and g precedes b in the second list, then it is a bad scenario and penalty of 1 is imposed. If the knowledge about the relative position of the b and g in the list is not known then a penalty of q is imposed and they are ranked as v + 1. The steps followed in GA optimization are as follows:

f(X) = H T ×

(10)

(X) +

where H T × (X) denotes the inner product. (X) represent the nonlinear mapping function which maps the inputs (X) to the higher-dimensional feature space. H represents the separating hyper-plane which maximizes the margin of the training data and is the bias. In order to solve this problem, the optimization problem represented in Eq. (11) should be solved.

i) The population size is initialised as a function of v and L i . ii) The objective function is computed for each member of the population based on Kendall’s distance. Then the members of next generation are selected using weighted random sampling where the weights are determined from the objective function score. iii) The selected members are then crossed-over for mixing the ordered lists and new solutions to the population pool are introduced by mutations that happen with mutation probability. If the solution obtained is maintained for consecutive generations, the algorithm is stopped. The choice of GA parameters such as cross-over probability, mutation probability, population size is important for convergence to optimal list.

N

min

H, ,

1 HH T + c (i+ 2 i=1

i

)

(11)

subject to the constraints

yi

(H T (xi))

+

i

H T (xi) +

0, i = 1, …, N,

yi 0

+

i i, i

(12)

Here, N is size of training sample, i, i are the slack variables which represent the upper and lower constraint on the dependent variable, c is the penalty factor associated to errors larger than . The performance of SVR depend on the choice of the hyperparameters c, , . The optimization problem can be solved by Lagrange multipliers and the solution is given by, 66

Applied Thermal Engineering 149 (2019) 62–72

S. Anitha Kumari, S. Srinivasan l

f(X) =

(n

n ) K (Xi,X)

n=1

1 2

where N represent the number of training data points.

l

(n

n )[K (Xr ,

n=1

Xn) + K (X s, Xn)]

7. Results and discussion

(13) n and n are the Lagrangian multipliers, l is the number of support vectors and Xr and X s represent the support vectors, K represent the kernel function.

7.1. Data collection and preprocessing The basic step in data based modeling is data collection and preprocessing. The RH2 data set used in this work is real time data obtained for a period of 5 months from 25-Aug-2016 to 14-Feb-2017 at an interval of 1 h from M/s Neyveli Thermal Power Plant. The data includes 9 soot-blow events and 30 predictors which includes flue gas input temperature (X1), flue gas output temperature (X2), steam input temperature (X3), steam output temperature (X4), combustion air flow (X5), coal flow(X6), load(X7), RH attemperator flow (X8) and metal tube temperatures from 22 sensors (X9-X30). The data hence obtained may be corrupted with outliers generated by process faults, sensor faults or human-related errors. A sample point in the data is considered as an outlier if the absolute value of the difference between the sample point and mean value of the data is greater than three times its standard deviation. Upon detecting a sample point as outlier, it is eliminated by replacing it with its mean or expected value. The outliers present in each variable are detected by 3-sigma rule and the percentage of outlier present in each predictor is shown in Fig. 4. The CF is determined using dual extended Kalman filter based parameter estimation whose initial parameters are tabulated in Table 1. It is observed from Fig. 5a that the CF shows a decreasing trend between soot-blows but inspite the soot-blow duration being constant the cleanliness level towards the end of each soot-blow varies. This is because the rate of deposition is non-uniform which is also confirmed from the corresponding box plot shown in Fig. 5b which shows different mean values between successive soot-blows.

6.2. Gaussian process regression Gaussian process is a collection of finite number of random variables which have Gaussian distribution and it is specified by mean and covariance function. GPR is a probabilistic regression technique which employs Bayesian methodology to derive the nonlinear model [17]. It assumes that the output of the regression model is dependent on the latent function f(X) and the Gaussian noise, with zero mean. The output of the regression model is given by Eq. (14) (14)

y= f(X) +

where the function f(.): . The latent function follows Gaussian distribution with a mean and variance given by, p

µ = K (Xt r , Xte)T (k (Xt r) +

= k (Xte)

(15)

2 I) 1y

K (Xt r , Xte)T (k (Xt r) +

2 I) 1K (X

t r,

Xte)

(16)

where K(Xtr , Xte) is the covariance between the training inputs and test point and k(Xtr) and k(Xte) is the autocovariance of the training and test point respectively. The covariance function reflects the presumptions about the latent function f(X) and so plays a very important role. Squared exponential covariance function expressed by Eq. (17) is the most commonly used covariance function.

1 2

K(Xt r , Xte) = exp

p

Wd (Xtrd

Xted ) 2

(17)

d=1

7.2. Variable selection

The hyperparameters of a Gaussian process with Gaussian kernel are { , W1, …Wp, 2} and their optimal value for a particular data set is obtained by maximizing the log marginal likelihood of the training data given by Eq. (18) using common optimization procedures say QuasiNewton methods

L ( , W1, …Wp,

2)

=

1 logdetK 2

1 T y K 2

1

y

N log2 2

In this work, five variable selection methods are considered namely RFG, UVE, PLS-VIP, RF and RLF. Table 2 tabulates the ranking of each variable by different variable selection methods. The rank aggregation was then applied to select the optimal variable subset with highest prediction accuracy. Fig. 6 shows a visual representation of the rank aggregation using GA. Fig. 6a shows the minimum values of the objective function at each iteration. It is seen that the algorithm has

(18)

Fig. 4. Percentage of outlier in predictor. 67

Applied Thermal Engineering 149 (2019) 62–72

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Table 1 Initial filter parameters of DEKF. Parameter

Matrix dimension

Value

P Q R T θ

10 × 10 10 × 10 2×2 8×1 2×1

diag{110−2 110−2 110−2 110−2 110−2 110−2 110−2 110−2 510−7 310−7} diag{110−4 110−2 110−4 110−2 110−4 110−4 110−2 110−2 110−8 110−8} diag{110−4 110−4} [600; 600; 600; 600; 500; 500; 500; 500] [0; 0]

Fig. 5. (a) CF determined using extended Kalman filter (b) Box plot of CF.

stabilized roughly after 11 iterations and the objective function has converged to a minimum score of 9.4. Fig. 6b represent the histogram of the objective function scores at the last iteration. These two plots give an idea about the rate of convergence of the algorithm and distribution of all the predictors at last iteration respectively. Fig. 6c displays the optimal ranking list which displays the optimal predictors as Flueout, Fluein, MT19, MT18, MT2. The real time data of the selected optimal variables is shown in Fig. 7.

7.3. Lag order selection The number of lag periods necessary to make each predictor significant is determined by observing the cross-correlation between the corresponding stationarized predictor and the stationarized dependent variable. The cross-correlation of flue gas input temperature with CF was found to be significant at lag 2 and flue gas output temperature at lag 5. Whereas, cross-correlation of MT2, MT18, MT19 were insignificant at all lags. This suggests that flue in, flue out, lagged by 2 periods and 5 periods respectively might be a significant predictor of CF, the dependent variable. Similarly the number of auto regressive terms

Table 2 Ranking of predictors using various variable selection algorithms. 'RF'

'RFG'

'UVE'

'VIP'

'RLF'

“Flueout” “Fluein” “MT11″ “MT17″ “Steam in” “Steamout” “MT1″ “attempflow” “MT22″ “coalflow” “MT20″ “MT16″ “MT13″ “MT2″ “MT7″ “load” “MT8″ “MT23″ “MT9″ “MT3″ “MT12″ “MT5″ “Airflow” “MT18″ “MT6″ “MT10″ “MT19″ “MT15″ “MT14″

“MT2″ “MT4″ “MT15″ “Flueout” “Air flow” “MT22″ “MT16″ “MT10″ “Flue in” “MT5″ “MT18″ “MT19″ “MT12″ “Steamin” “MT6″ “Steamout” “MT14″ “MT3″ “MT17″ “MT11″ “load” “MT13″ “coalflow” “MT9″ “MT7″ “MT1″ “MT8″ “MT20″ “MT23″

“Fluein” “Steamin” “attempflow” “MT20″ “MT19″ “MT2″ “coalflow” “MT1″ “MT4″ “MT6″ “MT16″ “MT12″ “MT18″ “MT22″ “Airflow” “Steamout” “MT7″ “MT3″ “MT11″ “MT13″ “MT17″ “MT15″ “MT5″ “MT14″ “MT9″ “MT23″ “MT10″ “load” “MT8″

“Fluein” “Flueout” “MT12″ “MT16″ “MT18″ “MT17″ “MT11″ “MT19″ “MT7″ “MT13″ “MT5″ “MT14″ “MT6″ “MT10″ “MT20″ “MT8″ “MT15″ “MT4″ “MT9″ “Steamout” “MT3″ “MT2″ “MT22″ “MT23″ “MT1″ “Steamin” “Airflow” “load” “coalflow”

“Flueout” “Fluein” “MT19″ “MT18″ “MT15″ “Airflow” “coalflow” “MT11″ “MT6″ “MT4″ “MT3″ “MT23″ “attempflow” “MT2″ “Steamin” “load” “Steamout” “MT12″ “MT9″ “MT20″ “MT22″ “MT10″ “MT8″ “MT14″ “MT17″ “MT7″ “MT16″ “MT1″ “MT5″

Variable ranking

“MT4″

“attempflow”

“Flueout”

“attempflow”

“MT13″

Bottom

68

Applied Thermal Engineering 149 (2019) 62–72

S. Anitha Kumari, S. Srinivasan

Fig. 6. Variable selection using GA (a) Minimum path (b) Final sample distribution (c) Rank aggregation.

algorithm. A linear kernel function has been chosen for the SVR model. The optimal values of the hyperparameters obtained during training are = 0.0083, c = 1, = 0.5238. Gaussian kernel function has been chosen for the GPR model. The optimal values of the kernel parameters obtained during training are = 1.1780 and 2 = 0.0430 for a log likelihood of 6.9295 × 103 . Table 3 shows the comparison of the developed models, which shows that NLARX model has the least RMSE compared to other models. It is observed that the RMSE value of the NLARX model at training is greater than at testing; an indication of a generalised model. The residual autocorrelation of the NLARX model as shown in Fig. 8a is found to be significant at lags 1, 2, 5, 6, 7 and 17, which violates the model assumptions. GPR model is a good fit to predict CF as it has reasonable accuracy and also the autocorrelation coefficients of the residuals are insignificant at all lags greater than 2 as evident from Fig. 8b. The model outputs are compared for the test set in Fig. 9, which shows that other than SVR, all the models are close to true value. 7.5. Soot-blow optimization In general the flue gas side of heat transfer surfaces are cleaned using steam soot-blowers, thereby allowing the boiler to operate at its peak efficiency. As it is difficult to estimate the ash fouling level of the heat transfer surface, soot-blowers in thermal power plant are initiated in a predefined sequence and schedule. However, during normal boiler operation, the soot-blow erosion rate is many times higher than the fly ash erosion [19]. Hence even short soot-blow periods may lead to serious damages of tubes more frequent soot-blow operation may lead to waste of steam and increased attemperator spray. Therefore, it is quite necessary to develop a new strategy to operate soot blowing and thereby maintaining the required level of heat transfer for the current boiler operating conditions. The following procedure of soot blowing

Fig. 7. Real time data obtained from power plant (a) Flue gas input temperature (°C) (b) Flue gas output temperature (°C) (c) MT19 (°C) (d) MT18 (°C) (e) MT2 (°C).

required for the model is found as 1. Hence, including the lag values of the selected predictors and the autoregressive term, there were totally 13 inputs. 7.4. Performance comparison of nonlinear models The obtained data is divided into two parts with 75% of the data (3040 samples) were chosen as training data set and 25% (1014 samples) were used as testing test. NLARX model with neural network nonlinearity is developed to estimate CF. A feed forward neural network architecture configured as 13–1−1 is chosen as the structure of the neural network. The activation function chosen for the hidden layer is tangent sigmoid function and linear activation function is chosen for the output layer. The NN was trained using Levenberg-Marquardt

Table 3 Comparison of nonlinear regression models.

69

Model

Training RMSE

Testing RMSE

NLARX SVR GPR

0.0135 0.0206 0.0042

0.0018 0.0223 0.0114

Applied Thermal Engineering 149 (2019) 62–72

S. Anitha Kumari, S. Srinivasan

Fig. 8. Residual autocorrelation (a) NLARX (b) GPR.

Qloss > QSB, the corresponding heat transfer coefficient is determined and CFcrtic can be obtained from

CFcritic =

Ut Uo

(10)

Ut represents the heat transfer coefficient at Qloss > QSB and Uo represents the theoretical heat transfer coefficient.2. Determine the soot-blow duration The soot-blow duration, δSB required to recover the clean level, CFclean will depend on the cleanliness factor itself. If the cleanliness factor at the end of fouling period is CFcritic then the soot-blow duration required to attain CFclean can be approximated by a linear function which is given by Fig. 9. Testing results of nonlinear regression models.

SB

optimization has been proposed.1. As an initial step, a critical value of CF, CFcritic should be established to activate soot-blow. It is determined by the fact that energy loss due to fouling (Qloss) should be equal to energy loss due to soot-blow (QSB). The energy loss due to fouling between successive soot blowing instant Δt is computed by

Q loss = Q clean

t

t

0

Qb (t)dt

SB (h si

hso)

CFclean

(11)

M

where M is the slope of the cleaning curve at CFcritic. The CF between successive soot-blow sequence of the real time data as shown in Fig. 10 is analysed using the proposed method. The decrease in heat transfer with increasing deposition is shown in Fig. 11. The energy loss due to soot-blow, QSB is calculated as 3.4 × 103 kJ/s. The above procedure is implemented and the corresponding threshold for CF is found to be 0.68. The amount of fuel saved is calculated by

(8)

Qclean represents the heat absorbed upon the maximum value of CF achieved after soot-blow and Qb represents the actual heat energy absorbed by the heat transfer surfaces. The energy loss due to soot-blow is given by

QSB = mSB

CFcritic

(9)

where δSB is the soot-blow duration, mSB is the soot-blow steam flow rate and hsi, hso are the steam enthalpy of soot-blower inlet and condenser inlet respectively. Upon determining the instant where

Fig. 11. Heat transfer between successive soot-blow.

Table 4 Impact of proposed soot-blow strategy.

Fig. 10. CF between successive soot-blow. 70

QSB (kJ/ s)

Actual soot blowing duration δSB, s

Calculated soot-blow duration, s

CFcritic

Fuel saved, tonnes/day

3400

3600

2880

0.68

3.23

Applied Thermal Engineering 149 (2019) 62–72

S. Anitha Kumari, S. Srinivasan

Net heat gain Calorific value of fuel

Fuel saved =

t

Net heat gain =

0

Q b (t)dt

monitor CF using an optimal set of exogenous variables. The optimal set of variables is obtained by GA based rank aggregation algorithm. The GPR model provided a close fit with RMSE of 0.0114 compared with NLARX and SVR. Further, an optimization strategy is proposed to initiate soot-blow operation based on the critical CF. The proposed method has resulted in an increased fuel saving of 0.16 tonnes/day.

(12)

Q SB

(13)

With the existing soot-blow strategy in power plants, the cleaning duration is about 3600 s and the maximum cleanliness obtained is 0.8, the amount of fuel hence saved is 3.07 tonnes/day. On adopting the proposed strategy, fuel saved is 3.23 tonnes/day as tabulated in Table 4. In conclusion, appropriate CF thresholds to initiate soot-blow as inferred in this work could lead to increased fuel saving of 0.16 tonnes/day.

Acknowledgement This work is supported by Department of Science & Technology, Government of India under DST-PURSE phase II programme -5.Manpower (Proc. No. 9500/PD2/2014, M.H.No.7.1.3.69).

8. Conclusion In this paper, nonlinear dynamic model is developed with an aim to Appendix A. Estimation of state and parameter using DEKF

Initialization: To initialize DEKF at k = 0, the mean value of the state and parameter and their respective error covariance are set as shown in following equations

(0) = E[ ] P (0) = E[( (0) T(0) = E[T(0)] Px (0) = E[(T(0)

(A.1)

(0))T]

(0))( (0)

(A.2)

T(0))T]

T(0))(T(0)

Computation: For k = 1,2,… compute Time update for parameter filter:

(k| k

1) =

P (k| k

(k 1| k 1P

1) =

(A.3)

1)

(k 1| k

(A.4)

1)

λ is the forgetting factor assumed in the range [0.9 1]. As time progress, λ disregard the previous information related to parameter uncertainties; without losing the current entries of P . This guarantees that the estimates are effectively modified by the innovations of measurement data. Time update for state filter:

T(k| k

1) = F(T(k 1),

Px (k| k

1) =

where

(A.5)

(k 1))

(k)Px (k 1| k

(A.6)

1) (k)T + Q

F T [T= T(k 1), = (k 1)]

(k) =

Measurement update for state filter:

K x (k) = Px (k| k

1)CT [CPx (k| k

T(k|k) = T(k| k

1) + K x (k)[y(k)

Px (k|k) = [I

K x (k)C]Px (k|

k

1)CT+R]

(A.7)

1

CT(k| k

(A.8)

1)]

(A.9)

1)

Measurement update for parameter filter:

K (k) = P (k| k (k|k) =

(k| k

1

(A.10)

1)]

(A.11)

1)(C )T [C P (k| k

1)(C )T+R]

1) + K (k)[y(k)

C T(k| k

P (k|k) = [I K (k)C ]P (k| k

(A.12)

1)

The main feature that distinguishes DEKF from JEKF is that the matrix C in the parameter gain K . C is defined as

(y(k)

C

CT(k| k

1))

=C

T(k| k

1) (A.13)

(k)

Unlike in state filter, the required linearization in the parameter filter will lead to the computation of recurrent derivative. This is because the state filter has a recurrent architecture, i.e., T(k) is a function of T(k 1) and both are functions of θ. The derivative of the state filter equation results in the following set of recursive equations:

T(k+ 1)

T(k)

=

F(T, ) T(k) T(k)

= (I Kx (k)C)

+

T(k| k

F(T, ) (A.14)

(k)

1) (A.15)

Assuming Kalman gain independent of θ. 71

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S. Anitha Kumari, S. Srinivasan

Appendix B. Supplementary material Supplementary data associated with this article can be found, in the online version, at https://doi.org/10.1016/j.applthermaleng.2018.12.031.

[9] L. Pattanayak, S.P.K. Ayyagiri, J.N. Sahu, Optimization of soot-blowing frequency to improve boiler performance and reduce combustion pollution, Clean Techn Environ Policy 17 (2015) 1897–1906. [10] V. Pihur, S. Datta, RankAggreg, an R package for weighted rank aggregation, BMC Bioinf. 23 (2009) 1607–1615. [11] S. AnithaKumari, S. Srinivasan, Extended Kalman filter for fouling detection in thermal power plant reheater, Control Eng. Pract. 73 (2018) 91–99. [12] L. Fortuna, S. Graziani, A. Rizzo, M.G. Xibilia, Soft Sensing for Monitoring and Control of Industrial Processes, Springer-Verlag, London, 2005. [13] K. Dziedziech, P. Czrop, W.J. Staszewski, T. Uhl, Combined non-parametric and parametric approach for identification of time-variant systems, Mech. Syst. Sig. Process. 103 (2018) 295–311. [14] E.A. Wan, A.T. Nelson, Kalman Filtering and Neural Networks, John Wiley & Sons, New York, 2001. [15] G. Jonsson, O.P. Palsson, K. Sejling, Modelling and parameter estimation of heat exchangers-A statistical approach, J. Dyn. Syst. Meas. Contr. 114 (1992) 673–679. [16] K.S. Narendra, K. Parthasarathy, Identification and control of dynamic systems using neural networks, IEEE Trans. Neural Networks 1 (1990) 4–27. [17] C.E. Rasmussen, C.K.I. William, Gaussian Processes for Machine learning, Available from, Institute of Technology Press, Massachusetts, 2006. [18] V. Vapnik, The Nature of Statistical Learning Theory, Springer, New York, 1995. [19] W. Wojnar, Erosion of heat exchangers due to sootblowing, Eng. Fail. Anal. 33 (2013) 473–489.

References [1] M. Mohanraj, S. Jayaraj, C. Muraleedharan, Applications of artificial neural networks for thermal analysis of heat exchangers, Int. J. Therm. Sci. 90 (2015) 150–172. [2] V.R. Radhakrishnan, M. Ramasamy, H. Zabiri, V. DoThanh, N.M. Tahir, H. Mukhtar, M.R. Hamdi, N. Ramli, Heat exchanger fouling model and preventive maintenance scheduling tool, Appl. Therm. Eng. 27 (2007) 2791–2802. [3] D.K. Mohanty, P.M. Singru, Fouling analysis of a shell and tube heat exchanger using local linear wavelet neural network, Int. J. Heat Mass Transf. 77 (2014) 946–955. [4] Y. Shi, J. Wang, Ash fouling monitoring and key variables analysis for coal fired power plant boiler, J. Therm. Sci. 19 (2015) 253–265. [5] B. Pena, E. Teruel, L.I. Diez, Soft-computing models for soot-blowing optimization in coal-fired utility boilers, Appl. Soft Comput. 11 (2011) 1657–1668. [6] M.U. Degereji, D.B. Ingham, L. Ma, M. Pourkashanian, A. Williams, Prediction of ash slaging propensity in a pulverized coal combustion furnace, Fuel 101 (2012) 171–178. [7] B. Pena, E. Teruel, L.I. Diez, Towards soot-blow optimization in superheaters, Appl. Therm. Eng. 61 (2013) 737–746. [8] Y. Shi, J. Wang, Z. Liu, On-line monitoring of ash fouling and soot-blowing optimization for convective heat exchanger in coal –fired power plant boiler, Appl. Therm. Eng. 78 (2015) 39–50.

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