Opportunities for the next generation of optical boiler diagnostics

Paper from the AFRC 2015 conference titled Opportunities for the next generation of optical boiler diagnostics

Inefficient boiler operation and control are responsible for wasting large amounts of fuel and releasing excess greenhouse gases (CO2 and N2O) and pollutants (CO, NOx). This is especially true in the United States where more than 80% of the energy used across all sectors is generated by fossil-fuels combustion. It is now recognized that continuous monitoring and control of both individual burners and groups of burners in boilers is essential to meet and sustain ever more stringent greenhouse and pollutant emission limits. This has become especially true as incremental improvements in burner performance have become disproportionately more difficult, and variations in fuel properties due to the widespread practice of fuel blending require frequent adjustment in burner settings to maintain optimum performance. One approach for advanced optical burner monitoring has been pioneered and successfully implemented commercially on coal-fired utility boilers by The Babcock & Wilcox Company. The Flame Doctor® system statistically characterizes dynamic information in the flicker signals captured by optical flame scanners to assess (and potentially adjust) the performance of individual burners or ensembles of burners (e.g., by mill group). While the value of this technology has been demonstrated repeatedly for over 12 years, it is inherently limited because conventional flame-scanner systems have been designed to meet very specific safety objectives and were never intended to be used for burner performance monitoring. In this work, we describe the current state of the art for burner diagnostics as embodied in the Flame Doctor system. Next, we present the theoretical basis for a new generation of advanced optical flame monitoring technology that could go well beyond the capabilities of current flame-scanner-based systems. We expect that the need for such capabilities will increase substantially as boiler fuel sources and needs for tighter emissions and efficiency controls continue to grow.

Finney, Daw, Fuller, Flynn, Kulp - Opportunities for the next generation of optical boiler diagnostics - AFRC 2015 Opportunities for the next generation of optical boiler diagnostics Charles E.A. Finney*, C. Stuart Daw Timothy A. Fuller, Thomas J. Flynn Christopher W. Kulp Oak Ridge National Laboratory Oak Ridge TN 37831 The Babcock & Wilcox Company Barberton OH 44203 Lycoming College Williamsport PA 17701 Inefficient boiler operation and control are responsible for wasting large amounts of fuel and releasing excess greenhouse gases (CO2 and N2O) and pollutants (CO, NOx). This is especially true in the United States where more than 80% of the energy used across all sectors is generated by fossil-fuels combustion. It is now recognized that continuous monitoring and control of both individual burners and groups of burners in boilers is essential to meet and sustain ever more stringent greenhouse and pollutant emission limits. This has become especially true as incremental improvements in burner performance have become disproportionately more difficult, and variations in fuel properties due to the widespread practice of fuel blending require frequent adjustment in burner settings to maintain optimum performance. One approach for advanced optical burner monitoring has been pioneered and successfully implemented commercially on coal-fired utility boilers by The Babcock & Wilcox Company. The Flame Doctor® system statistically characterizes dynamic information in the flicker signals captured by optical flame scanners to assess (and potentially adjust) the performance of individual burners or ensembles of burners (e.g., by mill group). While the value of this technology has been demonstrated repeatedly for over 12 years, it is inherently limited because conventional flame-scanner systems have been designed to meet very specific safety objectives and were never intended to be used for burner performance monitoring. In this work, we describe the current state of the art for burner diagnostics as embodied in the Flame Doctor system. Next, we present the theoretical basis for a new generation of advanced optical flame monitoring technology that could go well beyond the capabilities of current flame-scanner-based systems. We expect that the need for such capabilities will increase substantially as boiler fuel sources and needs for tighter emissions and efficiency controls continue to grow. Motivation and overall objective Utilities with coal-fired boilers are under increasing scrutiny and pressure to improve efficiency, thereby lowering greenhouse gas emissions, and to reduce pollutant emissions. The past two decades has seen significant progress in real-time monitoring of boiler flame and emissions performance, with several technologies currently in commercial implementation. In field testing during development of the Flame Doctor system, it was demonstrated how just one flame out of dozens in a boiler could severely affect overall boiler emissions and that having simple diagnostics of flame stability and state could enable boiler operators to make targeted changes with significant improvements, even when they lacked direct visual access to the poor-performing flames [Fuller 2004]. The state of the art in boiler flame monitoring has moved from time-averaged, usually linear, metrics to nonlinear metrics which account for the dynamical behavior of flames. Capturing both long- and short-timescale dynamical features of flames is important because many unstable and transient behaviors contribute disproportionately to poor combustion and emissions performance, and time-averaged metrics often do not quantify such events. With the continued development of hardware and software systems amenable for optical flame sensing in boiler furnaces, we are planning for the next generation of optical flame diagnostic systems. In this paper, we summarize highlights of some of the new approaches to boiler diagnostics that we expect to become prominent * EMAIL: [e-mail] TEL: [phone] Page 1 of 20 Finney, Daw, Fuller, Flynn, Kulp - Opportunities for the next generation of optical boiler diagnostics - AFRC 2015 in the near future. Common features that these new approaches are likely to share include more spatially extensive optical flame access, utilization of complex and nonlinear dynamical systems theory for interpreting flame patterns, and increased integration of online flame diagnostics with active boiler controls. Here we focus on pulverized coal flames in utility boilers, but many of the concepts could be applicable to other gas and oil furnaces where fuel-air mixing and flame structure are key to energy efficiency and emissions control. Brief overview of prior work The following discussion focuses on optical measurements of flames for diagnostic purposes. Other systems using non-optical measurements, such as with pressure, acoustic, or ionic sensors, or which do not directly measure flame properties, such as with flue-gas spatial analyzers, are not included. Commercially implemented systems While several ad-hoc schemes for measuring whole-flame images or signals from light-intensity sensors had been utilized informally for decades, in the mid-1990s commercial systems began to be developed which focused on statistical analysis of flame measurements. One such system was an optical system which used the Fourier (frequency-based) spectrum of flame flicker to assign a numerical quality metric [Khesin 1996a, 1996b, 1997]. The Fourier spectrum is linear and captures first-order effects on a time-averaged basis, but it does not capture all the nuances of dynamical variations seen in nonlinear systems such as flames in certain unstable combustion regimes such as with staged combustion of pulverized coal burners. Concurrently, techniques derived from the study of nonlinear dynamical and chaotic systems began to be applied to boiler flames [Fuller 1996a, 1996b]. Continued development under collaboration of the Electric Power Research Institute, The Babcock & Wilcox Company and Oak Ridge National Laboratory led to the development of the Flame Doctor system for commercial release in 2004 [Flynn 2003; Daw 2003b]. The Flame Doctor system utilizes flame-scanner signals, typically focused on a relatively small volume of the flame seen through a 10-15 cm (4-6 inch) diameter and several meter long sight tube, near the burner nozzle, and applies a series of statistical analyses of linear and nonlinear metrics to determine the relative stability of the flame. By using existing flame scanners installed for safety purposes or using custom scanners, the system can be quickly implemented on most utility boilers. The Flame Doctor system has been used on a temporary or permanent basis on dozens of utility boilers in both the US and internationally and has seen a good degree of success in identifying poorly performing burners. Correction of the boiler operation, largely in supervised open-loop control, either on a burner or mill-group basis has yielded very favorable improvements in boiler emissions (such as NOx and CO) by improving combustion quality. While this experience has had considerable value in improving boiler performance, ever more restrictive Environmental Protection Agency (EPA) boiler emissions limits demonstrate that enhanced optical sensors and improved dynamical characterization of flame, mill-group and overall boiler dynamics, reflecting the latest understanding of nonlinear dynamical systems theory, will be worth the development effort to achieve even greater improvement in boiler performance. Additionally, the latest EPA regulations recognize the importance of advanced closed-loop control systems; therefore, the integration of advanced sensors into these control systems will continue to be a priority. Page 2 of 20 Finney, Daw, Fuller, Flynn, Kulp - Opportunities for the next generation of optical boiler diagnostics - AFRC 2015 Recent laboratory and modeling studies in the literature Using optical sensors and images of flames to analyze flame states is not new. Marques and Jorge [Marques and Jorge 2000] used infrared images of flames to characterize flame shape and monitor flame characteristics in a boiler. Lu et al. [Lu 2004] used digital images of flames to measure several flame characteristics including flicker, temperature, and spreading angle. Digital images have also been used to analyze flames from a model industrial burner [Hernández and Ballester 2008]. The aforementioned cases involved studying features of the flame (such as shape) from the images. In some of the work described here, we will focus on generating time series data from the images (as in frame-by-frame analysis of a movie). Therefore, time series analysis algorithms can be applied to the images in order to gain information about the dynamics of the flame. Time series analysis algorithms have been successfully applied to time series generated by nonoptical measurements of combustion systems. Gotoda et al. [Gotoda 2012] used time series analysis algorithms and information theoretic analyses to study complexities in combustion instability for flames produced by a gas turbine combustor close to lean blowout. Time series analysis algorithms have been used to show that thermoacoustic oscillations transition to chaos in lean premixed fuel-air burners [Kabiraj 2012, 2015]. The time series in the aforementioned studies are not generated from images, but rather from measurements made directly from the flame or combustor (e.g. pressure fluctuations). However, both image analysis and time series analysis studies provide useful information about the dynamics of the flame. Hence, we expect that time series and information theoretic analyses on time series generated from images of the flame should produce important insights into the flame dynamics. Theoretical basis for the next generation of optical diagnostics In our 2003 presentation to the AFRC [Daw 2003b], we reported on the recent development of a commercial boiler flame diagnostic system. We recognized then that that system involved compromises both in the sensors used and in the analysis algorithms employed. In this section, we outline the potential for an improved diagnostic system based on enhanced sensors and enhanced signal-analysis techniques. Enhanced sensors Potential for whole flame measurements As mentioned previously, a major limitation of the current optical sensors is their limited field of view of the flame. This limited view severely restricts the ability of current diagnostic systems to adequately capture spatial information about the flame. The importance of the spatial information has been observed in practice on boiler flames where the structure of the flame within the optical sensor's field of view is dramatically different from the flame structure on the opposite side of the flame. In these situations, the Flame Doctor system incorrectly assesses the state of the flame. One way to address this limitation is to employ multiple optical sensors sighted on different parts of the flame. Another way to address this limitation is to image the entire flame using video cameras, where line of sight permits. Both approaches will not only provide flame structure information on different parts of the flame but will provide information on the correlation between different areas of the flame as well as the flow of information between those areas. As we discuss below, this type of information can be important in determining the onset of critical bifurcations. Most commercial utility-scale burners have multiple access ports on the burner front making implementation of the multiple optical sensor approach fairly straightforward. For example, burners are typically Page 3 of 20 Finney, Daw, Fuller, Flynn, Kulp - Opportunities for the next generation of optical boiler diagnostics - AFRC 2015 equipped with separate lighter and main flame scanners located approximately 180 degrees from each other. Most modern commercial boilers also employ special, high-temperature video cameras to allow the operators to view at least some of the flames. Locating video cameras to capture every individual flame in a large utility boiler can be difficult making this approach more challenging to implement than the multiple optical sensor approach. Potential for multispectral measurements The wavelength range of the existing flame scanners used by the current Flame Doctor system is fairly narrow. For coal and oil applications, the typical wavelength range of the scanners is from the upper visible spectrum to near infrared; approximately 600 to 1100 nm. For gas applications, the scanners are sensitive to wavelengths in the ultraviolet spectrum; typically less than 300 nm. For the next generation of optical boiler diagnostic systems, improvements could be made by employing multispectral sensors instead of using the existing flame scanners. We anticipate that analyzing and comparing time series data from different wavelengths using advanced techniques like those described below will provide important information on the dynamics of the flame. Multispectral optical sensors are already being used in commercial utility boilers though none are currently being used to assess individual flame performance. Optical pyrometers use the ratio of two different wavelength bands to calculate the temperature within the sensors field of view. Optical pyrometers are typically deployed in the upper part of the furnace to measure the temperature of the gases leaving the primary combustion zone. More recently, tunable diode laser (TDL) systems have been deployed in the upper furnace to simultaneously measure the concentrations of important gas species such as oxygen and carbon monoxide. Although these multispectral systems have been successful in their current applications, they would be difficult to utilize for individual flame diagnostics due to inherent limitations in their designs. Potential for multivariate measurements The focus of this paper is on optically-based diagnostic systems; however, the use of other measurements in addition to optical measurements has the potential to greatly enhance the performance of advanced flame diagnostic systems (for instance, see [Sanz 2008]). Pressure measurements, acoustic measurements, electrical measurements, and microwave measurements all have the potential to provide information about a flame's dynamics that cannot be gained from optical measurements alone. The potential benefits of a multivariate approach were demonstrated during the development of the Flame Doctor system in the 1990s. During pilot-scale testing of a single coal burner, we simultaneously collected pressure measurements in the coal transport line, pressure measurements in the air plenum, and acoustic measurements in the combustion chamber in addition to optical measurements of the flame. Analysis of these additional measurements revealed dynamical information similar to but not exactly the same as the dynamical information gained from the optical signals. More interestingly, correlating the different measurements with the optical measurements revealed additional insight into the combustion dynamics such as that information flow can actually be opposite to the physical flows of the fuel and air. Specifically, bivariate mutual information analysis was used to determine that ignition-extinction events as detected by an acoustic sensor in the combustion cavity were inducing pressure pulsations indicative of variations in the coal feed to the burner rather than vice versa. Page 4 of 20 Finney, Daw, Fuller, Flynn, Kulp - Opportunities for the next generation of optical boiler diagnostics - AFRC 2015 Enhanced signal analysis Anticipated improvements to the techniques currently implemented in the Flame Doctor system include exploitation of recent development of complex systems theory, the ability to characterize the flame dynamics behavior over spatial domains (such as described above), and the potential for adaptive learning for control systems. Complex systems often exhibit critical transitions (‘tipping points'), and these are often seen in the long-timescale shifts in pulverized coal boiler flames, particularly in cyclone burners with their long ‘memory' but also with wall-fired burners; being able to detect the approach or onset of an adverse critical transition could allow predictive control intervention to avoid the transition. In spatially extended systems such as a staged-combustion burner flame, accounting for the behavior of the larger-scale structures should improve characterization and prediction over spatially limited measurements, so developing techniques to account for spatio-temporal effects is important. Additionally, adaptive learning systems to account for longer-period (on the week or month timescale) routine variations in boiler operation (for instance, fuel composition, moisture or seasonal effects) can improve the effectiveness of diagnostic and control systems. Detecting critical transitions in complex systems The emerging science of complex systems is revealing important new insights into systems (both natural and manmade) that are made up of multiple dynamic, spatially extended, and interacting components. One insight of particular interest here is that flames exhibit the key features of complex systems, including the occurrence of ‘tipping points' or critical transitions (also sometimes called global bifurcations), which typically involve a sudden shift in the dynamic state as one or more parameters pass through critical levels. In the case of flames (and more broadly all combustion systems), such critical transitions are often associated with changes in fuel/air ratio (e.g., lean and rich ignition limits) or mixing (e.g., burner swirl and staging). The diagnostic concepts we describe here for boilers are based on the well-recognized occurrence of multiple types of abrupt transitions in burner operating state as one or more key parameters are varied. By understanding the unique dynamic features associated with each critical transition and how these features vary with distance from these transitions, previous work has already demonstrated that it is possible to use dynamic measurements of global burner flame luminosity variations to identify the proximity to one or more transitions. With this information, it is then possible to diagnose burner state and make appropriate control adjustments, both for individual burners as well as burner groups [Fuller 2014]. The key challenge in this process is to identify the most effective available burner measurements that are available and the most appropriate analytical algorithms for processing those measurements to detect the presence and proximity of critical burner states. A number of mathematical tools have been developed for understanding and diagnosing critical transitions in other fields (e.g., medicine [Liu 2012, 2014], ecosystems [Kéfi 2014; Lade and Gross 2012], climatology [Lenton 2008], and finance [May 2008]). The widespread applicability of these tools has been made possible by the underlying universality of the physical processes that drive critical transitions in complex systems [Scheffer 2009, 2012]. One general feature of these tools is that they are designed to detect specific temporal patterns in time series measurements of complex systems that are associated with critical transitions such as those illustrated in Fig. 1 (b-d). Flames in particular tend to exhibit so-called catastrophic bifurcations, which are characterized by a significant hysteresis (different equilibrium trajectory) associated with whether the transition is approached by change in conditions from above or below (to the left or right in the figure). Page 5 of 20 Finney, Daw, Fuller, Flynn, Kulp - Opportunities for the next generation of optical boiler diagnostics - AFRC 2015 Fig. 1. Response of system state to changes in conditions following the mapping function (bold curve), for (a) a near-linear system and for (b-d) various bifurcation scenarios associated with critical transitions in system states. (Reprinted by permission from Macmillan Publishers Ltd: Nature, Scheffer et al., 461: 53-59, 2009.) One particularly useful diagnostic feature in time series measurements of such systems is referred to as ‘critical slowing down' [Scheffer 2009]. In simple terms, this means that as a critical point is approached, the system state (as revealed by time series measurements) becomes increasingly slow in responding to small perturbations (e.g., in flames, this can be the luminosity or flame shape changes associated with flow turbulence or small, deliberate changes in fuel or air flow). Theoretical studies have shown that such slowing down typically starts relatively far from critical points and grows stronger as a criticality is approached. Thus the degree of slowing can provide an indication of distance from a criticality well before that critical point is actually reached. One widely used statistical indicator of slowing down is an increase in longer timescale autocorrelations. Other useful statistical indicators are increased variance and skewness [Scheffer 2009]. The former results when the system responses to small perturbations do not decay (because of the slowing) and thus the accumulating changes increase the state variance. The latter occurs because of the asymmetry in the system responses to perturbations toward or away from the critical point. One other notable feature of complex systems approaching a critical transition is referred to in the complexity literature as ‘flickering'. This use of the term is distinct from what is typically meant in describing flames, although there probably is a more direct correspondence in some cases. In the literature, flickering refers to a condition where there is the potential for bimodality in the statistical distribution of the system state, as one would expect to observe when a system is pushed back and forth across a critical transition (e.g., separating two very different regimes) by stochastic perturbations. So critical combustion transitions that result in two distinct flame states (e.g., lifted vs. attached flames) could be classified in this context as flickering. Page 6 of 20 Finney, Daw, Fuller, Flynn, Kulp - Opportunities for the next generation of optical boiler diagnostics - AFRC 2015 Besides distinctive temporal patterns, the approach to critical transitions is also often associated with the development of non-uniform spatial patterns. Many complex systems (and flames clearly) can be seen as consisting of numerous local but coupled units or zones, each of which assumes a state influenced by the states of the zones around it. The resulting spatial coherencies can take the form of localized patches or fronts that move or oscillate in characteristic ways as the critical point is approached. These spatial features can take various forms in flames, including oscillatory shifts in flame shape or size, alternating bright and dark zones, and variations in color [Maxworthy 1999; Biagioli 2007; Annunziato 2000; Huang and Yang 2004]. Because the spatial patterns for each type of critical transition are typically very system specific, there is no ‘one size fits all' that applies to all transitions and all systems. For burner diagnostics, however, this is actually advantageous, because it provides a mechanism to discriminate between the different possible flame types (i.e., different criticality regions) and thus improve the ability to resolve particular burner conditions and potentially diagnose the root cause of a combustion stability problem. As explained in the following discussion, we believe that the addition of spatial pattern characterization to the suite of tools used to interpret optical signals is one of the most promising new developments in the field of boiler diagnostics. Algorithms for characterizing spatio-temporal information Spatio-temporal information can be obtained from spatially extended systems such as a flame by combining time series measurements from different spatial regions. One example, which will be further illustrated below, is based on using optical sensors to record the color of different parts of a flame as a function of time. The color can be recorded as numerical values as described below. Using the tools of symbolic time series analysis [Daw 2003a], spatio-temporal information can then be obtained from the multiple time series generated from various regions of the system. While the application of symbolic analysis is not a requirement, it is often useful in complex or noisy environments. In symbolic time series analysis, a time series is transformed into what is called a symbolic time series whose elements consists of a few discretized symbols (sometimes called an alphabet). For example, a binary symbolization would transform a time series into a series of 1's and 0's. The resulting symbolic time series can then be analyzed to obtain information about the underlying dynamics generating the series. See Fig. 2 for an example symbolization of a scalar time series. Of particular interest are information theoretic quantities such as the Shannon entropy [Shannon 1948] and the transfer entropy [Schreiber 2000]. Page 7 of 20 Finney, Daw, Fuller, Flynn, Kulp - Opportunities for the next generation of optical boiler diagnostics - AFRC 2015 Fig. 2. Illustration of (a) partition-based binary symbolization and grouping of sequences into coded words, and (b) resulting frequency distribution of symbol sequences. (Figure from [Daw 2000]). Symbolization can be done using a variety of means. One of the simplest techniques is by binning the data using thresholds (as demonstrated in Fig. 2). There are many different techniques for choosing and handling thresholds. For example, returning to the idea of binary symbolization, one can use the mean of a time series as the threshold and any element greater (less) than or equal to the mean would be assigned the symbol 1 (0). Ideally, the chosen threshold would be a generating partition which would guarantee that the resulting symbolic time series accurately captures the underlying dynamics producing the time series [Bollt 2000]. However, identifying a time series' generating partition can be difficult in practice. An alternative method of symbolization is known as the Bandt and Pompe (BP) methodology [Bandt and Pompe 2002]. The BP methodology is a dynamic, difference-based symbolization which partitions the time series into subsets of length d (with overlap d - 1) and then maps those subsets to permutations of the set {1, 2, … d}. The permutations are called ordinal patterns and each ordinal pattern can be assigned an integer from 1 to d! in order to simplify the symbolization. BP symbolization is robust to noise, takes into account causal relations in the data, and avoids the aforementioned issues of threshold dependencies. In the work described below, thresholds were used for symbolization, however an extension of the work using the BP methodology is a planned avenue of future research. Once a time series has been symbolized, various information theoretic analyses can be applied to the resulting symbolic series in order to better understand the system's underlying dynamics. One such algorithm is the Shannon entropy [Shannon 1948]: Page 8 of 20 Finney, Daw, Fuller, Flynn, Kulp - Opportunities for the next generation of optical boiler diagnostics - AFRC 2015 𝐻𝑆 = − ∑ 𝑝(𝑠)log⁡(𝑝(𝑠)) 𝑠 where p(s) is the probability of the symbol, s, appearing in symbolic series, and the sum is done over all symbols in the series. The Shannon entropy gives a measure of the information content of a series and can be thought of as the average information gained with each new measurement. The base of the logarithm provides the units of information. For example a base-2 would have units of bits. In general, series with high Shannon entropies are considered to correspond to more complicated dynamics than series with a lower Shannon entropy. A series of all one symbol would have HS = 0 (p(s) = 1 and log(1) = 0); whereas a random series, where all symbols are equally probable, would have HS = log(N), with N being the number of symbols in the series. Many information theoretic quantities are built from the Shannon entropy. The basic idea is that by replacing the probabilities in the Shannon entropy with joint probabilities, causal relations can be obtained either between elements in a series or between two different series. An example of such an algorithm is the transfer entropy [Schreiber 2000] which measures the rate information is exchanged from series X to series Y: (𝑘) 𝑇𝑋→𝑌 = (𝑘) (𝑗) ∑ 𝑝 (𝑦𝑖+1 , 𝑦𝑖 , 𝑥𝑖 ) 𝑙𝑜𝑔 ( (𝑗) 𝑝 (𝑦𝑖+1 |𝑦𝑖 , 𝑥𝑖 ) ) (𝑘) 𝑝 (𝑦𝑖+1 |𝑦𝑖 ) where the sum is done over all possible symbols, subscripts correspond to their series, and the (𝑘) superscript identifies a subset of past values from the series (i.e. 𝑦𝑖 = {𝑦𝑖 , … , 𝑦𝑖−𝑘+1 }). Typically, k = j = 1, for computational efficiency. If one wants to compute the transfer entropy from Y to X, then interchange the x's and y's in the above formula. Information is said to be exchanged from X to Y if 𝑇𝑋→𝑌 > 𝑇𝑌→𝑋 . In addition, it is common to check to see if 𝑇𝑋→𝑌 > 𝑇𝑋→𝑌̃ , where 𝑌̃ is a random reordering of the series, Y. The additional step can help determine if there is a false identification of information transfer due to small sample effects [Marschinski and Kantz 2002]. In fact, it is common to use an effective transfer entropy, 𝑇𝑋→𝑌 − 𝑇𝑋→𝑌̃ [Marschinski and Kantz 2002] when working with short time series in order to illustrate a clear information transfer between series. In the case of spatially-extended systems, it is possible to obtain temporal and spatial information simultaneously using an extension of the techniques described above. First, the system must be spatially-partitioned, i.e. distinct non-overlapping regions of the system are identified. Then, from each region, a time series is generated using the local measurements. Then, each time series can be symbolized and information theoretic metrics computed to quantify the temporal patterns. Continuing our earlier example of a flame, a windowed Shannon entropy for each region of the flame can be used to characterize how the dynamical complexity changes for of various regions of the flame. Furthermore, computing the transfer entropy between time series generated from neighboring regions can reveal how information is shared or transported between those regions. When all the regions in a flame are considered simultaneously, it is possible to quantify the global flow of information throughout the flame. Adaptive learning and integration with control systems Dynamical control systems with static parameters or set points often cannot adapt to normal baseline shifts in the system behavior. Utility boilers can experience such shifts quite routinely, for instance, with changes in fuel blending, moisture content, and seasonal variations or constraints such as emissions limits. Additionally, subtle changes in mill operation, air distribution, or burner settings can result in flame dynamical changes, and control systems trained on the patterns seen at Page 9 of 20 Finney, Daw, Fuller, Flynn, Kulp - Opportunities for the next generation of optical boiler diagnostics - AFRC 2015 one baseline might not respond optimally, or even accurately enough to diagnose the boiler state, at another baseline condition. Adaptive learning systems have been employed in various forms for decades. Examples of these include expert systems and neural networks; however, the framework of these schemes are often not suited to accommodate the types of multidimensional metrics associated with some of the more advanced signal-analysis techniques described above. A type of diagnosis system useful for boiler flame measurements as described above should be selfaware. That is, not only should it accurately quantify the flame behaviors, it should constantly assess the stationarity of the boiler ensemble and re-learn the system as needed. There are many ways to achieve this end; here are two of interest:  Using the ensemble of burner statistics in relation to a previously benchmarked state, particularly in the context of overall performance metrics (such as emissions data)  Using the statistics of burners relative to each other compared with previously benchmarked inter-burner relations In the first case, knowing when the ensemble ‘normal' (but acceptable) has changed is important. In the second case, tracking the interrelation of individual burner behavior can help highlight instances and perhaps causes of shifts in boiler operation. Especially important is monitoring shifts in the context of critical transitions (as described above) and doing so in time to avoid a transition into an adverse condition. This could be particularly effective in diagnosing a rogue burner within a group of burners that are serviced by a single mill. Example experimental observations In this section, we focus on a simple laboratory gas burner to demonstrate certain concepts which could be relevant to boiler flame measurements. These concepts include how to characterize multispectral measurements (using visible color planes as examples), how to generate and numerically analyze time series from these measurements, and how to quantify information flows in the flame (either within a single flame or among adjacent flames). Our group has performed preliminary experiments in order to understand how to characterize spatio-temporal information in a flame. These experiments are on the level of "proof-of-concept" and are intended to illustrate the application of the information theoretic algorithms described above. In this section we describe our experiment, discuss how to generate time series from video, and demonstrate some calculations that can be done with the resulting time series. In the end, the goal is to provide information about the dynamics of the flame. The experiment The experimental facility is located at Lycoming College. The experiment used a High Temperature Blast Burner (H-5020) sold by Humboldt Mfg. Co. The burner burns a premixed fuel-air mixture. The flame was confined. The fuel was laboratory-supplied natural gas, and an air compressor supplied the air. Air and fuel flows were measured by analog flow meters and pressure gauges. It is important to note that since laboratory-supplied air is used, exact air-fuel ratios (AFR) are unknown since the composition of the natural gas is unknown. Because the experiment was intended only to demonstrate the application of the information theoretic algorithms, knowledge of the specific AFR was not critical. Future experiments will involve better fuel sources and hence better AFR measurements. Our data for this experiment comes from video recordings of the flame. The flame was recorded using a Canon EOS Rebel T3 DSLR with an EFS 18 - 55 mm lens in .mov format and at a rate of 30 frames/second. Page 10 of 20 Finney, Daw, Fuller, Flynn, Kulp - Opportunities for the next generation of optical boiler diagnostics - AFRC 2015 Generating time series from video recordings Video recordings of the flame were used to generate time series data. The data were generated directly from each frame of the video. One can think of an image as being stored as a matrix of pixels. Therefore an image with a resolution of 400 pixels  600 pixels is stored as a matrix with 400 columns and 600 rows. Each matrix element (or pixel) contains a pixel value, a number or triplet that is used to store information about the part of the image within that pixel. If we think of an image as a matrix of values (either constants or triplets), then we can produce a time series by recording the value of each pixel in each frame of the video. Hence each pixel provides a time series. A 10 second video recorded at a resolution of 400 x 600 would give 24,000 time series (400 times 600), each of which are 300 elements long (10 seconds times 30 frames/second). In regards to the previous discussion on spatio-temporal information, the image was divided into regions (pixels) and a time series was generated from each region (pixel values). Pixel values can be stored in a variety of ways using different color spaces. A common color space is RGB where each pixel is represented by a triplet of integers, {R, G, B}, that range from 0 to 255. For example, the color red would be {255, 0, 0} while white would be {255, 255, 255}. So an RGB image can be thought of as a matrix of triplets. Another color space is grayscale where each pixel is represented by an integer ranging from 0 to 255 where 0 is black and 255 is white. It should be noted that some software use a normalize grayscale in which black is given the value 0 and white is given the value of 1. The advantage to working with grayscale is that each pixel is represented by only one number so generating a time series from each pixel is easy. The disadvantage of grayscale is that one loses color information in the transformation from RGB to grayscale. However with grayscale, information on the light intensity is retained. Deciding how and when to use RGB or grayscale is an avenue for future research. While it is possible to generate a time series for each pixel, we are often only interested in the pixels that contain the region of interest. In this case, we are video recording a flame. Focusing only on the flame pixels makes the calculation more computationally efficient. However, it also leads to the challenge of having the computer distinguish between the background and the flame. To aid in this distinction, the flame is recorded in front of a black background, which should have the RGB value {0, 0, 0} or grayscale value of 0. Noise in the camera's CCD can prevent one from simply filtering out all pixels whose value is {0, 0, 0} or 0. Hence, a threshold has to be established in order to distinguish between the flame and background. The choice of threshold is difficult because if it is set too high, the algorithm may mistakenly identify parts of the flame as background, especially for dim flames. In addition, flames flicker and sometimes pixels do not remain in the flame or in the background for the entire video. In our preliminary experiments using grayscale, we disregarded noise effects, which were small, and identified any pixel with a value of 0 as a background pixel. Any pixel whose value is 0 for the entire video is considered part of the background and is not included in calculations. For RGB-based calculations, we disregarded any pixel whose maximum value in the triplet was less than 10, admittedly an arbitrary choice. Studying the effects of the choice of background threshold is an avenue of future research. Once the time series data has been obtained from each pixel, the time series needs to be symbolized in order to perform information theoretic calculations. In the work described here, we performed information theoretic calculations only on grayscale data. A threshold-based symbolization was used in which pixels with a grayscale level of 0 were assigned the symbol, 0. Pixels that had grayscale values greater than or equal to 0.2 were assigned the symbol 2 and values greater than 0 but less than 0.2 were assigned the symbol 1. Note that a normalized grayscale was used for pixel values. Three symbols were chosen in order to distinguish the background from flame pixels. The threshold value of 0.2 was chosen because it was the mean of the pixel data for most of the flame Page 11 of 20 Finney, Daw, Fuller, Flynn, Kulp - Opportunities for the next generation of optical boiler diagnostics - AFRC 2015 pixels. However, future work is needed in better determining thresholds, especially when dealing with the RGB color space. Now that we have explained how to generate a time series from video, we will illustrate some of our preliminary results. We will show results for calculations using both RGB and grayscale data. Mean value calculations As mentioned previously, each image is stored as a matrix of pixels. A simple calculation would be to compute the mean pixel value for each image. We call this calculation a mean value calculation. We used the RGB color space so each image had three mean values, one for R, G, and B. The goal of this calculation was to see what we could learn about the flame dynamics from the color of the flame in each frame. The basic idea was that a flame in a steady state would have fairly constant color, whereas a flame whose dynamics are changing may go through a color change. This, in fact, can be seen in the next two figures. Fig. 3 shows the mean value calculation for a flame in a steady state, the AFR is fairly constant and lean. In Fig. 3, the color of the data corresponds to its color channel, for example, the blue line corresponds to B. Fig. 4 shows a frame from the video used to generate Fig. 3. From Fig. 4 it is clear that the most dominate color in the flame is blue and hence, the B coordinate has the highest value throughout the video. A more interesting case appears in Fig. 5 where we see a spike then decrease in each color channel. In the experiment used to produce Fig. 5, the flame started out in a rich state so that there was quite a bit of red color to the flame. Fig. 6 is a sample frame from the video used to generate Fig. 5. At about 150 seconds into the experiment, the amount of air being fed to the burner was increased and the flame transitioned to a lean state. The final state of the flame was similar to that shown in Fig. 4, however the air was increased to a point where the flame all but blew out. The data in Fig. 5 show a clear change in the mean values due to the change in AFR. Whether or not this kind of data can be used to detect critical transitions in the flame's state is still an open question and is a future avenue of research. Page 12 of 20 Finney, Daw, Fuller, Flynn, Kulp - Opportunities for the next generation of optical boiler diagnostics - AFRC 2015 Fig. 3. The mean value calculation for a flame with a steady air-fuel ratio. The color of the data corresponds to its color channel. Fig. 4. An image of the flame corresponding to Fig. 3. Page 13 of 20 Finney, Daw, Fuller, Flynn, Kulp - Opportunities for the next generation of optical boiler diagnostics - AFRC 2015 Fig. 5. The mean value calculation for a flame with an air-fuel ratio that changes at about 150 seconds into the video. The color of the data corresponds to its color channel. Fig. 6. The early stage of the flame used to generate Fig. 5. Shannon entropy calculations Next, we focus on calculations intended to reveal spatial information about the flame. For simplicity in calculation, we convert the video to grayscale and produce time series for each pixel as described above. The video was 30 seconds long (300 frames) and frames of the video were cropped down to an image 95 pixels by 186 pixels. The cropping was done in order to reduce the number of background pixels and speed up calculations. We computed the Shannon entropy for each pixel's time series and produced a grayscale image. That image is shown in Fig. 7. The intensity of each pixel in the resulting image is proportional to the Shannon entropy of that pixel. A Page 14 of 20 Finney, Daw, Fuller, Flynn, Kulp - Opportunities for the next generation of optical boiler diagnostics - AFRC 2015 black pixel corresponds to a Shannon entropy of 0. The video used for this calculation is the same as the one used to generate Fig. 3. Fig. 7. The result of a Shannon entropy calculation. The intensity of each pixel is proportional to that pixel's Shannon entropy. Notice that in Fig. 7, the edge of the flame tends to have the highest Shannon entropy. That is likely due to the fact that the border of the flame was not physically stationary. The brightness of the core of the flame did not vary much in the video and hence has a smaller Shannon entropy. The black area at the base of the flame is actually the burner's opening. That opening can be seen as a bright blue oval in Fig. 4. The color of that region did not change during the video, hence the Shannon entropy corresponding to that region is 0. Fig. 7 tells us something about the spatial distribution of information in the flame throughout the video. It does not tell us anything about how that distribution of information changed as a function of time. We repeated the calculation for a windowed Shannon entropy. For a windowed calculation, the time series was generated from the video as before, however, now each pixel's time series is windowed, or partitioned into subsets. Window lengths can be chosen based on the timescale of interest in the problem. Furthermore, the window must be long enough such that there is an appropriate sampling of the symbols. The more symbols that are used in symbolization, the longer the window needed to ensure accurate statistics are captured in the window. In the work done here, a window length of 300 was used, which corresponds to 10 seconds of video. The windows overlap by 299 elements. The Shannon entropy of each pixel's window was computed and an image was formed for each set of windows. The result is a video whose frames are similar to that of Fig. 7, but for 10 seconds of video as opposed to the entire video. In fact, the resulting video consisted of frames that look very much like Fig. 7. In other words, the spatial distribution of information did not change with time. This is to be expected since the flame's AFR was not changed during the experiment. The results here are preliminary but do show us a path to which we can obtain spatio-temporal information about the flames dynamics. Exploring the Shannon entropy for flames with a varying AFR is an avenue of future research. Transfer entropy calculations Unlike the Shannon entropy, the transfer entropy can tell us how information is transferred from one region of a flame to another. For this analysis we used the same grayscale video and symbolization used in the Shannon entropy calculation. For simplicity, we start by describing the Page 15 of 20 Finney, Daw, Fuller, Flynn, Kulp - Opportunities for the next generation of optical boiler diagnostics - AFRC 2015 methodology of a non-windowed transfer entropy calculation. After generating the symbolic time series for each pixel, we can compute the transfer entropy between the time series generated by a pixel and the one immediately above it (stopping at the top row). From these transfer entropies; we can generate an image describing the direction of information flow throughout the flame. If information from a given pixel is transferred to the one above it (i.e. 𝑇𝑏𝑒𝑙𝑜𝑤→𝑎𝑏𝑜𝑣𝑒 > 𝑇𝑎𝑏𝑜𝑣𝑒→𝑏𝑒𝑙𝑜𝑤 ), we color that pixel red. If a pixel received information from the one above it, we color the pixel blue. If no net information was transferred (i.e. 𝑇𝑏𝑒𝑙𝑜𝑤→𝑎𝑏𝑜𝑣𝑒 = ⁡ 𝑇𝑎𝑏𝑜𝑣𝑒→𝑏𝑒𝑙𝑜𝑤 ), then the pixel is colored white. The result is then an image that shows how information is transferred between pixels throughout the flame. If the video is short, then the effective transfer entropy could be used instead. Because we are interested in spatio-temporal information, we need to window the time series of each pixel. We followed the procedure described above for the windowed Shannon entropy, where we partitioned each time series into windows of length 300 and an overlap of 299. The shortness of the windows required us to use the effective transfer entropy to ensure that detected information transfer was not due to small sample effects. The effective transfer entropy was computed using the first window of each pair of pixels (a pixel and the one immediately above it) and an image was produced in a method similar to that described above. The result was an image illustrating the direction of information transfer between neighboring pixels during the first 10 seconds (300 frames) of video. Next, the second window was used for each pixel and the process was continued. By the time the last window was reached, we had a set of images that can be animated. Hence, the final result is a movie whose frames compose of an illustration of the direction of information transferred between each pixel and the one above it. A frame of such a movie is shown in Fig. 8. Notice that the scales of the images are not the same. The image on the left is a frame captured from the grayscale video of the flame. The image on the right is a frame of the video produced by the windowed transfer entropy analysis. The first frame of the transfer entropy video corresponds to the frame 300 of the flame video. So the transfer entropy frame below is created using the first 300 frames of the flame video. The second frame of the transfer entropy video is created from frames 2-301 of the flame video, and so on. The image on the right shows both red and blue pixels, demonstrating a detection of information flowing both up and down in the flame. The white region near the base in the transfer entropy video roughly corresponds to the bright base of the flame seen in the left, which is actually the opening of the burner. Fig. 8. A frame of a video generated by performing a windowed transfer entropy analysis. The left image is of the flame and the right image is the result of the windowed transfer entropy. Fig. 8 is intended to illustrate the idea behind the analysis described in this section. The results are preliminary and no conclusions have been arrived at from this analysis at this time. However, it is our hope that such an analysis will prove useful in identifying and predicting behaviors in the flame Page 16 of 20 Finney, Daw, Fuller, Flynn, Kulp - Opportunities for the next generation of optical boiler diagnostics - AFRC 2015 such as critical transitions or flame blowout. For example, this technique could be used to detect the presence or absence of recirculation flow of combustion gases to the root of the flame in the fuel-rich core of a low-NOx burner, which is essential for maintaining flame attachment. However, in order to gain such insights more work needs to be done, as highlighted above. Another calculation that can be done with the resulting transfer entropy video is to count the number of red and blue pixels in each frame. Fig. 9 shows the pixel count for the video whose frame was used to make Fig. 8. In Fig. 9, the color of each data set corresponds to the color of the pixel counted. We see that in this particular case, information tended to be transferred upwards as opposed to downwards during the video. The type of graph shown in Fig. 9 may be more useful than producing a transfer entropy video because it is often easier to see trends in a graph than to detect trends in a video. Fig. 9. Time history of the number of red and blue pixels in a transfer entropy video. The procedure described above need not be restricted to a transfer entropy analysis and Shannon entropy. Similar analyses can be done using mutual information, or any other analysis. The central point of this section, however, is to provide a method of generating time series data from a video recording of a flame. Once the time series is generated, any time series analysis algorithm or information theoretic algorithm may be applied potentially providing global information on the structure of the flame. Conclusions and recommendations Currently implemented boiler flame diagnostic systems have shown that real-time monitoring of combustion performance, on a per-flame and/or mill-group basis, can yield significant improvements in combustion quality and thus improve emissions and increase efficiency. Page 17 of 20 Finney, Daw, Fuller, Flynn, Kulp - Opportunities for the next generation of optical boiler diagnostics - AFRC 2015 Continued improvement to optical systems should reflect recent advances in hardware, software, and dynamical-systems theory. Taking advantage of the current state of the art in imaging and computational hardware, the next generation of optical sensors for boiler flames may incorporate some of the following features:  Wider field of view (either whole flame or near-nozzle, as available)  Greater spatial resolution, providing images for analysis rather than overall flicker intensity signals  Wider or multiple spectrum, incorporating visible, IR, and UV in multiple channels, to take advantage of each detector's sensitivity to different aspects of the combustion physics  Multivariate sensors, for instance, to consider effects of pressure/acoustic fields in addition to the optical flame qualities, or using multiple optical sensors with different views of the flame Both empirical experience and dynamical systems theory strongly suggest that it should be possible to go beyond simple classification of individual flame states to predictive identification of global boiler performance trends, either in response to imposed plant operational changes or as a result of inherent system transitions. Implicit in the notion of prediction is that there is some sort of causal model (either physical or statistical) based on which the likelihood of future boiler states can be deduced from the present and/or past states. There are a variety of such model-based predictive approaches, each with different qualities depending on their focus, but approaches which account for the boiler system's global behavior should be favored over those that focus only on local flame assessments. In doing so, integration into automatic boiler control systems will be easier and more effective. The ability of online control systems to adaptively update prediction models and appropriate responses under evolving system constraints will be critical in practical commercial implementations. The next generation of optical boiler diagnostic systems should help continue the trend of increased efficiency and tighter emissions control in boilers. Although we have focused on pulverized coal boilers, many of the theoretical concepts are applicable to oil and gas boilers and furnaces. Acknowledgements Babcock & Wilcox and Oak Ridge National Laboratory acknowledge the support of the Electric Power Research Institute during the development of the Flame Doctor system. We also recognize and acknowledge the contributions of engineers from Alliant Energy, Ameren, and Southern Company during the initial field trials of the Flame Doctor system. Disclaimer This manuscript has been authored by UT-Battelle, LLC, under Contract No. DE-AC05-00OR22725 with the U.S. Department of Energy. The United States Government retains and the publisher, by accepting the article for publication, acknowledges that the United States Government retains a non-exclusive, paid-up, irrevocable, world-wide license to publish or reproduce the published form of this manuscript, or allow others to do so, for United States Government purposes. 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