Image Based Monitoring for Combustion Systems

Transcription

1 Image Base onitoring for Combustion Systems J. Chen, ember, IAENG an.-y. Hsu Abstract A novel metho of on-line flame etection in vieo is propose. It aims to early etect the current state of the combustion system an prevent the system from further egraation an occurrence of failure. he propose metho consists of hien arov moel (H) an multiway principal component analysis (PCA). PCA is use to etract the cross-correlation among spatial relationships in the low imensional space while H constructs the temporal behavior of the sequence of the spatial features. he probability istribution of the normal status can be traine by the images collecte from the normal operation processes. he propose metho can generate simple probability monitoring charts to trac the progress of the current transition state sequence an monitor the occurrence of the observable upsets. o emonstrate the performance of the propose metho, ata from the monitoring practice in the real combustion systems are conucte. Ine erms Combustion Systems; Hien arov oel; ultiway Principal Component Analysis; Statistical Process Control I. INRODUCION he inustrial furnaces, such as fossil fuel-fire furnaces, are wiely use to prouce electrical power by combusting ifferent fuels []. any combustion problems, incluing poor flame stability, low combustion efficiency an high pollutant emissions, shoul be consiere. herefore, the monitoring of combustion processes have become highly esirable to monitor, estimate an even reuce the levels of pollutant emissions [,3]. One traitional way to monitor the combustion process is flame watch by eperience worers. Nevertheless, the rawbacs are that it is har to quantify the combustion performance only by human eperience an the woring environment is usually too poor [4]. emperature is a general measurement ine to monitoring the combustion process. he conventional temperature monitoring evices, such as thermocouples an pyrometers, are single-point measurement an cannot provie the temperature istribution of the flame. With the current evelopment of optical sensing an igital image processing techniques, on-line continuous monitoring of the flame is becoming possible by a spatial an his wor was sponsore in part by National Science Council, R.O.C. an in part by the project owar Sustainable Green echnology in the Chung Yuan Christian University, aiwan, uner grant CYCU-98-CR-CE J. Chen is with Department of Chemical Engineering, Chung-Yuan Christian University, Chung-i, aiwan 3, Republic of China (corresponing author to provie fa: ; jason@ wavenet.cycu.eu.tw)..-y. Hsu is with Department of Chemical Engineering, Chung-Yuan Christian University, Chung-i, aiwan 3, Republic of China. cost-effective way [3]. Some researchers evelope statistical sensitivity methos to monitor the combustion process. Yan et al. () etracte the geometrical an luminous features of the pulverize coal flames to quantify the combustion process an i sensitivity analysis []. hey emonstrate that some image features coul help etect the change of combustion processes. However, most research focuse only on the point estimation without consiering the region of operating istribution. Whereas an incipient fault occurs in the operation combustor, fault information is often wea; it is ifficult to etract wea fault information using irect analysis of the image ata because in practice, the flame flicer frequency is not constant an it varies with time. herefore, it is necessary to create a new process control metho to monitor the combustion process. Hien arov moels (H) are recognize as being appropriate for time sequence ata. In a H moel, each observation is the ata sequence epening on the previous elements in the sequence. An H is capable of characterizing a oubly embee stochastic process with an unerlying stochastic process that can be observe through another set of stochastic processes because the state of the system is not observable irectly [5]. With the inspiration of the H framewor, a statistical moel of spatiotemporal ynamic process variables for the sequence images is evelope using H an PCA in this paper. he ynamic ata array is constructe by incorporating both static an ynamic image characteristics using the prior an the current images. he strongest relations of the scores are etracte by PCA. With the etracte scores, the H moel can be integrate into the eisting PCA metho to enhance the capability of statistical process monitoring. hus, the control chart for a two-imensional image is evelope in this research. he chart is not only an analysis the two-imensional spatiotemporal measurements but also capture the statistical characteristics of the practical ata. II. PCA-H BASED ODEING FOR DYNAIC IAGES Flame images ehibit spatially homogeneous repetitions an temporally ynamic patterns. he repetition is the pattern of the burning flame that changes regularly its amplitue, form an color. he sequences of images show a regular pattern repetition an ynamic behavior because this repetition can be foun in time as well as in space. his means that each flame image is seen as a point in a given subspace, following a trajectory as time evolves. he moeling ynamic images can locate an appropriate subspace to represent the trajectory an ientify the stochastic

2 trajectory with a metho of ynamic stochastic theory. In this research, an integrate image-base moel that maes use of two statistic techniques, PCA an H, to escribe the spatial an temporal behavior is propose for monitoring the operation combustors. PCA is use to etract the spatial features of the trajectory in a smaller space while H is use to train temporal behavior using a ynamic probability moel. A. Spatial Feature Etraction: PCA he ata set of a sequence of τ images can be arrange as a two-imensional array as shown in Fig.. Assume each color image of the size is N N an the original color encoing is RGB. It can be reshape into a sequence of column vectors of the length N N 3. With a sequence of τ color images, the column vectors ( R,,, τ ) are orere from top to the bottom in a two-imensional array X R τ τ, where lower inices inicate that the matri collects frames from to τ. he temporal mean of each piel is compute an subtracte from X, an a new matri Y is obtaine. o get the information on the variability among the images, PCA is performe, t t t tr t t t t R tτ tτ t tτ τr an P [ p p p ] R () is the loaing matri. his means that imension reuction is performe by retaining the first R single value of the ecomposition. hus each frame is written as y yˆ + e t p + t p + + t p + e R R his means that y ˆ is a linear combination of the columns of matri P, which contains the basis of the subspace onto which the image vector y is projecte. he columns of matri P contain the eigenvectors whose linear combination generates one flame image. he score vector t fies the weights of the linear combination, so the features of image frames change in time are etracte. e represents the resiual error. (3) N time Image τ 3NN time τ B. emporal Feature Etraction: H H illustrate in Fig. is a ouble stochastic moel, where the non-boe circles represent a sequence of observations. When H is applie to the combustor system, the metho for moeling sequential image ata is the chain structure that captures interaction between a sequence of inputs, N S S S Y τ S i S i i Fig.. Unfole structures of the ynamic tetures S R r r + + r Y t p E P E () o o o where R is the number of principal components, E is a resiual matri, an represents the score matri Fig.. Graphical moel for H with the sequential variables o t, t, tr, v (4) where o consists of etracte r, t, r,,, R over the first R components of at time point an the

3 corresponing resiual variation at time point, which is efine as v ee o capture the interaction in the sequence ata, the number of the past τ observation is use to train H. First the feature ata from the PCA ecomposition, { o o oτ } is collecte. In Fig., there is a set of hien variables, s { S,, }, an a fie number of states ( ). he probability P( o ) can be written as a sum of term P( os ) over all the possible state sequences, P( o) P( o s) P( o s) P( s) K all s s Π P( o S ) P( S S ) s he transition istribution ( PS ( S ) ) is efine as PS ( j S j) a, j, j jj hus the probability of the transition, A { a jj } (5) (6) (7), is an state transition probability matri. Note that at the starting point, the initial state istribution, Π { π j } an π j PS ( j). he observation istribution ( P( o S) ) is characterize by a miture of Gaussian ensity an H P( o S j) c N( μ, Σ ) jh jh jh h H jh jh K h c, c, j,,, where H is the number of mitures. c is the weight for each miture component but it shoul sum up to for each state. Each Gaussian probability ensity function is an elliptically symmetric ensity with the mean vector μ jh an the covariance matri Σ jh c jh, jh, jh parameters are { } (8). he observation probability B μ Σ. For etail in miture of Gaussian istribution, please refer to [6]. hus, the H moel parameters are λ [ A B Π]. he etail of the training algorithm can be foun in [7]. Given the above optimization for etermining the H λ A B Π, it is necessary to return to the parameters, [ ] assumption that the winow size ( ) is nown. o etermine the winow size, the H problem shoul be solve in Eq. (6) for several values of, with the value of giving the lowest ispersion of a stochastic process, min H ( ) min p( o )log( o ) o being the best estimate of the winow size. he above equation, so calle entropy, is a unifie probability measure of uncertainty quantification. he main avantage of entropy is that it provies a general escription of stochastic system without constraints of certain istribution [8]. his approach, which is essentially a search in one irection, is require because the variable ( ) is iscrete, so it is not possible to etermine the analytical erivation of H ( ) with respect to the winow size. he technique is iterative in nature an the search proceure is terminate when minimal relative improvement ( ( H ( ) H ( ) ) H ( ) ) is less than a preset value. o S S S S S S o o S S S o I o τ + oτ + S S S S S o S S oτ b^ h h ( h ( ), ) opt t b P O S λ (9) observation (O) O Ω bo.95 Fig. 3. he optimal state sequence in bol line in the traine moel for each ata set an the probability of the selecte optimal state at the en time point of the moving winow forms a istribution. III. ONIORING CONRO CHAR BASED ON PCA-H Once the H moel is traine, the most liely state sequence for an observe sequence coul be foun. For a given moel an an observation sequence O o o o, the most liely unerlying state { } + * * * * + sequence ( ( s ) { s s s } ) can be foun * ( ) { + } + s s s s arg ma P( O, s λ) + * * * + s () A recursive Viterbi algorithm with ynamic programming can be use to fin the most liely state sequence [9]. he same proceure is repeate for all the collecte sets to compute the most liely state sequences for each set. Fig. 3 shows the single best state path for each set. Not all the sets follow the same best path. Different selecte states for ifferent sets account for the fact that the observe values of

4 the process variables o not perfectly conform to the eterministic moel. his variability is resulte from the uncertain variations an isturbances among the luring variables that affect the system. For on-line monitoring of the observation images, the control limits shoul be built for normal operation. As the new image is taen, the image ata from the beginning till the current time point ( ) are available ( Y ( ) ) Y( ) y + y y () ime he score matri by projecting the ata ( Y ( ) loaing matri ( P ) can be compute:,,, R t t, t, t, R ) onto the ( ) Y( ) P () t t, t, t, R ( ) (3) t t t t he portion of the ata ( Y ( ) ) corresponing to the R smallest singular values forms the resiual variation v e e ( ) v v e e v ee e ( ) ( ) I PP Y e e (4) (5) Fig. 4. he eperimental combustion system. IV. EXAPES A schematic iagram of the eperimental furnace with a flame-monitoring system is shown in Fig. 4. he burner of the eperimental furnace uses inustrial heavy oil as fuels. he air source of combustion comes irectly from a irect-riven air compressor. A igital color camera is installe to capture the images of flames in the furnace. he camera with the specifications of piels an a resolution of 4 bits per piel is capable of capturing flame images at 73 frames per secon. he output signal of the camera is sent to a computer in IEEE-394a interface an the imaging sample rate is set as one frame per four secons consiering the computer loaing hen concatenate the score vector t n an the variation v n, n,,, sequentially to mae a sequence pool O { o o o}. With the evelope probability istribution that reflects the normal operation, the control limit for the selecte state at each time point is require to etect any eparture of the process from its stanar behavior ( ( ) *, λ ) > ( ) * P ( o s, ).95 th P s P λ o o (6) Relative improvement Winow size () Fig. 5. Entropy of the observation probability his integral is approimate by bootstrapping the original sequential ata set to generate enough ata an obtain truly quality-relate variables from the sequential process ata. For more information on the bootstrapping, please refer to wor by []. he ata corresponing to 95% of the th confience limit is taen to get a lielihoo threshol ( P ). he propose metho is implemente real-time on a lap-top an teste for a large variety of conitions in comparison with the metho utilizing only the color variation information. A total of image ata which is not use as a testing set in this case stuy is collecte to buil the moel when no eterministic isturbances are ientifie in the operating log. In PCA-H, the time-sequential image ata set is unfole in a two-imensional array (shown in Fig. ). hen this matri is ecompose by PCA, an via cross-valiation, it is foun that 7 principal components are neee to escribe the ata set. his moel captures 98.64%

5 of the variation in the process ata set. hen, temporal sequential ata are constructe using the etracte features from PCA moel. During training H, the ifferent winow sizes of H are applie. Fig. 5 shows the entropy of the observation probability ecreases with the increasing number of winow sizes. hus, the selecte winow size of H is 7. he control charts of the moels for the normal operation are shown in Fig. 6, where the control limit of log P( o λ) is obtaine from the propose PCA-H. he control limits representing 95% an 99% confience limits are also shown in Fig. 6. -log P (a) ime (b) observe images, incluing the first 3 images in the normal conition an the rest 3 in the abnormal one, is use for etection. For the abnormal conition, the monitoring outcomes of the propose moel are shown in Fig. 6. he initial time of the fault is inuce at the 3 th point. As shown in Fig. 6, even though the abnormal process with small isturbance eists, the fault can still be etecte after PCA-H is applie to characterizing the temporal opt ynamics between images. P( o S ) has been increase remarably an it has fallen outsie of the 95% confience limit after the 3th time point. he small etection lag is ue to the transport elay of the air flow. If the complete training ata structure is irectly applie to H without variable reuction, the number of observe variables are more than 978 at each time point. he H moel with 3 hien states woul result in parameters, which are a prohibitively large number. It is impossible to train the moel. he problem is usually encountere when we have a moerately large number of observe variables. It can be alleviate by the propose metho. In this stuy, the number of parameters in PCA-H is 5, which is significantly less than that in H only. he smaller the number of parameters is fitte, the faster the moel training woul be converge an the less ris of overfitting the training ata woul have. hus, it eplains why H is use to construct the temporal behavior of the variables after PCA in the propose metho. 9 8 (a) 7 -log P (b) ime (c) Fig. 6. (a) he testing ata monitore by PCA-H control charts of the normal operating conition with 95% (ash line) an 99% (soli line) confience limits. he first 3 points are normal an the rest (from 3 to 6), abnormal; (b) zooming in on the ata aroun the control limits. wo abnormal conitions, which are two ifferent levels of fee air rates linearly ecreasing uring two ifferent perios of time, are use for testing. For easy visualization an comparisons, time-sequential images in one normal conition an two abnormal ones are shown in Fig. 7. However, ifferences between the normal (Fig. 7(a)) an the minor abnormal (Fig. 7(b)) operating behaviors can not be istinguishe from the image ata irectly. he spatiotemporal correlations in the image are not apparent because flame flicer frequency which is not constant incurs the variations in flame piels. o save space limitation, only the minor fault conition is use for testing. he set of 6 Fig. 7. ime-sequential images where the interval between the images is three minutes: (a) normal; (b) abnormal with the minor fault conition; (c) abnormal with the major fault conition V. CONCUSION Abunant real-time igital image ata can be gathere in the automatic system. Particularly, in this wor, the igital RGB flame images collecte from the combustor contain the compleity an uncertainty of the process behavior. he volume of image ata being generate an processe eeps growing an there appears no en in sight to this tren, so mining an fusing a series of universal applicable quantities from the historical ata to monitor the operation status is essential. his will help combustion control as well as reuce

6 fuel consumption. In this paper, H base monitoring is propose. However, the use of H in on-line image analysis has up to now been limite to the area of the tet an speech recognition. Since the sequences of images from combustors can be regare as simply two-imensional signals with the inepenent variables repeate in the time frame. In this research, the conventional multivariate PCA are etene by incorporating the H structure to solving the etection problem for the two-imensional repetition observation. In orer to quantitatively iscriminate the operation istribution, PCA-H is applie at the moeling probability istribution stage. he spatiotemporal patterns can be traine. he corresponing control limits that evaluate the current process can be estimate. Even though the sequence image has a two-imensional spatial relationship an a temporal behavior, the comparisons of quantitative an qualitative results of the propose metho are mae through a real eperimental problem for investigating the feasibility of the propose PCA-H metho. he propose metho may be incorporate with ifferent surveillance systems for image monitoring an early etection. REFERENCES [] Y. Yan, G. u, an. Colechin, onitoring an characterisation of pulverize coal flames using igital imaging techniques, Fuel, 8, pp [] J.. Beer. Combustion technology evelopments in power generation in response to environmental challenges, Prog. Energy Combust Sci., 6, pp. 3-37,. [3].Gang, Y. Yong an C. ie, A igital imaging base multifunctional flame monitoring system, IEEE rans Instrum eas., 53, pp [4] H. Zhang, Z. Zou, J. i an X. J. Chen, Flame image recognition of alumina rotary iln by artificial neural networ an support vector machine methos, Cent South Univ echno., 5, pp.39-43, 8. [5].R. Rabiner, A tutorial on hien arov moels an selecte applications in speech recognition, Proc. IEEE, 76, pp.57-86, 989 [6]. itchell, achine earning, cgrew Hill, New Yor, 997. [7] J.. ee, S.J. Kim, Y. Hwang an C.S. Song, Diagnosis of mechanical fault signal using continuous hien arov moel, J Soun Vibrat., 76, pp.65-8, 4. [8] A. Papoulis, Probability, ranom variables an stochastic processes, 3 r e., New Yor: cgraw-hill, 99. [9].D. oore, ost iely state sequence speech reconstruction using a generalize Hien semi-arov moel with two istinct regeneration times applie to English, Ph.D issertation, Rensselear Polytechnic Institute, 4. [] B. Efron an R. J. ibshirani, An introuction to the bootstrap, Chapman & Hall, onon, 993.