Local anomaly detection in hybrid rocket combustion tests

Despite being born at the same time of solid and liquid propulsion systems, hybrid rocket engines are still not a mature propulsion technology. Only in recent years, there has been a renewed interest in hybrid propulsion due to its characteristic safety, cost and environmental advantages. Due to the fact that the propellants are stored in two different states of matter, hybrid motors are safer than solids. This also contributes to the reduction in the total costs of the engine. Moreover, they are characterized by controllable thrust, including shutoff and restart capability. With respect to liquid engines, they are mechanically simpler and, consequently, cheaper (Karabeyoglu et al. 2011). Finally, their performance is in between those of solid and liquid engines. Unfortunately, due to the characteristic diffusive flame mechanism (the propellants are not premixed, but they need to gasify and mix with each other before being able to react), this technology presents some disadvantages, like poor regression rate performance for conventional polymeric fuels (resulting in low thrust level), time-varying parameters and scaling difficulties. However, most of these drawbacks can be solved by employing a correct design process. In particular, in order to increase the burning rate, the so-called liquefying hybrid rocket fuels, such as paraffin-based ones, can be used. These fast burning fuels are characterized by low viscosity and surface tension and they experience a different combustion mechanism with respect to conventional polymeric fuels (Karabeyoglu et al. 2001). During the combustion, they are able to form a thin liquid layer on the fuel surface, which may become unstable because of the high-speed oxidizer gas flow. The instability waves of the fuel melt layer (Kelvin–Helmholtz waves) may break up and cause the entrainment of fuel droplets into the gas stream. This enables an additional fuel mass transfer and, consequently, an increase in the burning rate (Karabeyoglu et al. 2002). The entrainment mechanism works like a spray injection along the length of the motor, which increases the effective fuel burning area and reduces the blocking effect given from the pyrolysis of the fuel. Unfortunately, this phenomenon has not been well understood yet and still needs to be fully characterized.

For a better understanding of the entrainment process and its relation to the regression rate, optical investigations on the combustion behavior of paraffin-based fuels burning with gaseous oxygen have been performed. The combustion tests have been recorded with a high-speed video camera, and at the end of the test campaigns, a large amount of data has been collected. Therefore, an automatic analysis method is needed in order to get a faster and deeper insight into the combustion process. An overview of the different flow phases can be obtained by an automatic clustering of the dataset (Rüttgers et al. 2020). This gives essential information on the mean burning behavior. However, in order to completely understand the combustion mechanism, it is important to detect entrained droplets and irregular flow and flame structures, such as Kelvin–Helmholtz waves, appearing during the burning time. The identification of the point in time when such phenomena are showing up could help in understanding the operating conditions leading to an increase in the regression rate. Depending on the fuel composition and oxidizer mass flow rate, a different amount of entrained fuel droplets, as well as different turbulent scales and structures characterizing the flow and the flame, are expected. Even if these turbulent structures only exist within a short period of time, they might strongly affect the overall burning behavior. Therefore, in order to identify specific combustion phenomena, it is necessary to detect “anomalies” in the dataset. In this study, the local outlier factor algorithm is applied to the combustion data.

The remainder of this article is organized as follows: First, a short introduction on the local outlier factor (LOF) algorithm is given in Sect. 2. In Sect. 3, the experimental setup that is used to obtain the combustion dataset is described. Finally in Sect. 4, the relevance of the chosen algorithm for the current dataset is justified by comparing it to other outlier detection algorithms. Furthermore, a detailed investigation of different crucial parameters used in the LOF algorithm is presented. Lastly, an analysis of the experimental combustion data, based on the outcome of the anomaly detection algorithm, is given. The analysis provides detailed insights into the “anomalies” appearing during the combustion process. In particular, LOF is able to identify specific processes, such as the entrainment of fuel droplets into the gas stream and the flame fluctuations during the transients. The detection of the point in space and time where these phenomena appear during the combustion is important to better understand the whole burning process in liquefying hybrid rocket fuels.

Various definitions of outliers exist in the literature, mostly in the area of statistics. One established definition of an outlier  (Hawkins 1980) states that it is an observation deviating so much from the other observations that it could be generated by a different mechanism. This definition, however, bases on a global view on the dataset. Consequently, it primarily covers anomalies that can be described as global outliers. In our application on high-speed image data, the dataset also contains flow features that are only outliers with respect to their local neighborhoods, i.e., the time frame shortly before and after the anomaly. A specific example in this application are represented by melted fuel droplets that only cover small areas of the images and do not significantly change the average image brightness. In the literature, outliers deviating only with respect to their neighborhoods are often denoted as local outliers and an algorithm that allows for detecting local outliers is required.

In this manuscript, local outlier factor (LOF) (Breunig et al. 2000) is employed as one viable algorithm to detect local outliers. A further justification for using LOF is given in Sect. 4.1 for a simplified 2D representation of the original dataset. In contrast to global outliers, labeling an observation as a local outlier or not depends on the specific application so that a local outlier can be an inlier in other situations. Consequently, local outliers are outliers only up to a certain degree. The LOF algorithm assigns an outlier factor to each image, i.e., a floating point value \(>0\), where the size of the numerical value indicates the degree of being a potential outlier.

In the following, the basic definitions of LOF are stated. The core concepts of LOF are the k-distance of an object and the reachability distance (Breunig et al. 2000). Let d(a, b) be a distance measure, while a and b denote images in the dataset. Then, the k-distance(a) is the distance of a to its kth nearest neighbor. The complete set of the \(k\in {\mathbb {N}}\) nearest neighbors includes all images with a distance \(\le\) k-distance(a) and is written as \(N_{k}(a)\). Note that the cardinality of \(N_{k}(a)\), denoted by \({\text {card}} \left( N_{k}(a)\right)\), can be larger than k if several images have the same distance with respect to a. Next, the reachability distance from a to b is defined asNote that Eq. (1) does not specify a mathematical distance since it is not symmetric. The motivation for Eq. (1) is to define a dissimilarity measure that is robust against statistical fluctuations. These fluctuations occur for very similar images with small distances. For these images, the actual distance is replaced by k-distance(b). The size of the hyperparameter k controls the smoothing effect. For \(k=1\), the usual (unsmoothed) distance measure \(d(\cdot , \cdot )\) is recovered. The local reachability distance (\({\text {lrd}}\)) of an image a is defined asEquation (2) defines the inverse of the average reachability distance of image a. Interestingly, if image a has at least k duplicates, i.e., the \({\text {reach-dist}}\) of all duplicates is zero, Eq. (2) tends to infinity. In our application, this potentially occurs before and after the test, when all images are black and have zero distance with respect to each other. For this reason, these images without information have been removed from the dataset. Finally, the local outlier factor (LOF) of a is defined asLOF specifies a degree to which a is an outlier based on comparing the local reachability distances of the neighbors. Three different situations can occur in Eq. (3):Therefore, if \({\text {LOF}}_{k}(a)>1\), a is a potential outlier. On the other hand, \({\text {LOF}}_{k}(a)\le 1\) indicates potential inliers.

In the following, the advantages and disadvantages of LOF will be discussed. The main disadvantage of LOF is that the ratio defined in Eq. (3) is hard to interpret by the user. Moreover, the threshold value C to separate inliers (images a with \({\text {LOF}}_{k}(a)<C\)) from outliers (images b with \({\text {LOF}}_{k}(b)>C\)) is problem dependent and has to be separately determined for each combustion test. The authors of the LOF algorithm have suggested several approaches to allow for a better interpretation of the outlier factor. One possible extension is called local outlier probability (LoOP) that scales the LOF ratio to a value range [0, 1] (Kriegel et al. 2009) so that a single threshold value for inlier/outlier separation can be better determined. However, since all combustion tests in this manuscript are evaluated in detail with specific threshold values, this extension is not required here. A further disadvantage is that the correct choice of the hyperparameter k, which controls the smoothness of the distance measure, has to be found. However, since the LOF outcome varies smoothly with k, it is sufficient to determine the correct order of magnitude of the hyperparameter in most applications. In Sect. 4.3, the choice of k for this specific application is considered. On the other hand, LOF has several advantages. The main advantage of LOF is that the algorithm is able to detect local outliers that would be ignored by global anomaly detection algorithms. Furthermore, LOF only requires that \(d(\cdot , \cdot )\) is a dissimilarity and not a distance function, i.e., the triangle inequality is not required. Finally, LOF is able to cope with regions of different densities. If, for instance, several high-density regions in a dataset exist, LOF might label a point with a medium density in these clusters as an outlier. This coincides with our application since we expect different combustion phases, such as an ignition, a steady combustion and an extinction phase, which all form high-density clusters. Even then, LOF is still able to detect outliers in all different phases.

The quality of the algorithm for finding anomalies primarily depends on the quality of the dissimilarity measure \(d(\cdot , \cdot )\). An adequate choice simplifies a separation of abnormal images from the images showing regular flow conditions. Furthermore, since each pixel of the image dataset represents a further dimension, the algorithm has to deal with high-dimensional data. In the literature, a lot of effort is spent on anomaly detection for high-dimensional data (Zimek et al. 2012). This is due to the fact that distance or dissimilarity measures are often less effective in high-dimensional problem spaces. For this reason, two different dissimilarity measures will be used in this manuscript: an Euclidean norm (discrete \(L^2\)-norm) and a dissimilarity measure that bases on a structural similarity index measure (SSIM) (Wang et al. 2004). According to the literature, \(L^1\) and \(L^2\) are the most adequate \(L^p\)-norms in high-dimensional spaces (Hinneburg et al. 2000). On the other hand, SSIM has been specifically developed for image comparisons and it is one of the most used algorithms in imaging science. Let a and b denote images in the dataset, the SSIM index of these images is defined aswith \(\mu _{a}\) as the mean brightness of a (analogously for image b), \(\sigma _{a}^2\) as variance of a, \(\sigma _{a,b}\) as the covariance of a and b and \(c_1\), \(c_2\) and \(c_3\) as variables to stabilize the division with small denominators. \(c_1\), \(c_2\) and \(c_3\) only depend on the dynamic range of the pixel values and are identical in all tests since images with an 8-bit dynamic range are always considered. As illustrated in Eq. (4), SSIM is the product of three comparisons that investigate the difference in luminance l, in contrast c and in structure s of a and b. SSIM is a similarity measure ranging from zero to one. A dissimilarity function, the structural dissimilarity \({\text {DSSIM}}\), is obtained by a linear transformation according toSince \({\text {DSSIM}}\) bases on a threefold comparison of the images, it has a larger computational complexity than an Euclidean norm. In Sect. 4.2, the performance of both measures to find anomalies in the test dataset will be compared.

Note that both distance measures do not contain knowledge from combustion theory and detect all possible image changes. Using domain knowledge, i.e., knowledge on how an image that shows an anomaly differs from an inlier images, more adapted distance measures, which are able to better separate inliers from outliers, could be constructed.

The combustion tests were performed at the German Aerospace Center (DLR), Institute of Space Propulsion in Lampoldshausen, at the test complex M11. An already existing modular combustion chamber, used in the past to investigate the combustion behavior of solid fuel ramjets (Ciezki et al. 2003), was adjusted and used for the test campaigns at atmospheric pressure. A side view of the whole combustion chamber setup is shown in Fig. 1. The optically accessible combustion chamber is 450 mm long, 150 mm wide and 90 mm high. The flow straighteners with the pre-chamber are in total 450 mm long and the post-chamber is 150 mm long. The oxidizer main flow is entering the combustion chamber from the left, after having passed two flow straighteners, in order to get homogeneous flow conditions in the burner. The mass flow rate is adjusted by a flow control valve and it is measured with a Coriolis flow meter. A high-frequency static pressure sensor is mounted in the combustion chamber. Ignition is done via an oxygen/hydrogen torch igniter from the bottom of the chamber. At the end of the combustion, after having closed the main oxidizer valve, nitrogen is used for purging. A test sequence is programmed before the test and is run automatically by the test bench control system. More details about the test bench and test settings are given in Kobald et al. (2015), Petrarolo and Kobald (2016), Petrarolo et al. (2018).

In the framework of this research, all tests were run at atmospheric pressure and with an oxidizer mass flow ranging from 10 to 120 g/s. Combustion tests were performed using a single-slab paraffin-based fuel with a \(20^{\circ }\) forward facing ramp angle (see Fig. 2), in combination with gaseous oxygen. Two different fuel compositions were analyzed in this study: As baseline, pure paraffin 6805 from the manufacturer Sasol Wax was used; furthermore, 5% of a commonly available polymer was added to it in order to change the fuel viscosity. All fuel slabs, produced and machined according to the same procedure, were 200 mm long, 100 mm wide and 20 mm high. Burning time was 3 seconds for each test. For video data acquisition, a Photron Fastcam SA 1.1 high-speed video camera with a resolution of \(N = 1024 \times 336\) pixels was used. The frame rate was set to 10,000 frames per second, thus being able to catch all the important combustion and flow phenomena. The shutter time of the camera was adjusted for each test, according to the test conditions (especially brightness) and position of the camera. Tests were also performed using a CH* chemiluminescence imaging technique, with a band-pass filter centered around 431 \(\mathrm {nm}\) placed in front of the camera. The excited CH* molecules emit photons around this wavelength, when they relax back to a lower energy state. Since high CH* concentration exists only in the main reaction zone, the resulting images provide a good indication of the instantaneous flame sheet location and topology.

In this study, three combustion tests have been analyzed. The test matrix is presented in Table 1.

Local outlier factor was chosen as one viable algorithm to detect local anomalies in the dataset and applied to hybrid combustion data. To the best of our knowledge, this is the first application of local outlier detection in the specific application of hybrid rocket combustion. The analysis demonstrated that this algorithm is able to reveal several interesting phenomena appearing during the combustion and clearly indicates the potential of unsupervised learning techniques for the study of large datasets. In this work, it was proved that the detection of local anomalies is able to recognize specific phenomena characterizing the combustion of liquefying hybrid rocket fuels. In particular, fuel droplets get entrained into the oxidizer flow and burning over the flame are clearly identified as outliers with respect to the main combustion process. Furthermore, the first appearance of the flame over the fuel slab surface during ignition, the extinguishing flame after the nitrogen purge, as well as flame blowing and fluctuations during the steady combustion are recognized as weaker disturbances to the regular flow. Depending on what the user is interested in investigating, some parameters can be tuned in the algorithm. The number of neighbors k that is considered by the algorithm influences how “local” the outcome is: By increasing k, the detected outliers range from short-time disturbances to whole combustion phases (thus becoming almost a clustering algorithm). Moreover, in the post-processing phase, the user can choose the threshold value separating the inliers from the outliers, thus deciding which phenomena have to be considered as important anomalies and which ones are only background noise (like soot formations and light reflections on the window, in this case). In this study, it was also shown that, depending on the dissimilarity measure used in the algorithm, the detected anomalies may vary. In particular, the Euclidean metric gives good results in finding local luminosity changes, even of few pixels (see Fig. 5), and therefore, it is particularly suitable to detect burning fuel droplets. On the other hand, the structural dissimilarity measure (DSSIM) is more sensitive to a general frame luminosity variation, and therefore, it is able to detect only strong variations from the main flow, such as a huge amount of droplets or a large flame movement. These characteristics makes the DSSIM distance metric more robust against undesired camera movements, such as shaking, during the test. Strong anomalies, like flows of burning droplets or a fast change in the combustion flame, are detected by both distance measures.

The intention of this work is to demonstrate that unsupervised learning techniques can be successfully applied to large combustion datasets in order to identify specific flow phenomena. In the future, other outlier detection algorithms can be applied to the complete imaging dataset and compared to the LOF algorithm. Moreover, the authors will further develop unsupervised, as well as supervised, learning techniques to apply to combustion data. The objective is to get detailed information on the important phenomena characterizing the hybrids combustion process, such as the entrainment. The next step will be to train the algorithm how to automatically recognize particular structures, such as Kelvin–Helmholtz waves, vortices and droplets, in space and time.