Reaction Wheel Performance Characterization Using the
Kepler Spacecraft as a Case Study
Jennifer L. Kampmeier∗, Reidar J. Larsen∗, and Lucas F. Migliorini∗
Laboratory for Atmospheric and Space Physics, University of Colorado Boulder, Boulder, CO, 80303
Kipp A. Larson†
Ball Aerospace & Technologies Corporation, Boulder, CO, 80301
The Kepler spacecraft had lost two of its four reaction wheels by 2012, and the Kepler attitude engineers were forced to create a novel concept of operations to continue the mission. Monitoring the health and performance of the surviving wheels became a critical task, as loss of another wheel would be mission-ending. To support these efforts, a group of students at the Laboratory for Atmospheric and Space Physics developed, verified, and refined an analysis tool to identify changes in reaction wheel behavior. The tool compares the data we are interested in analyzing to a verified set of baseline data, then filters the comparison to further highlight trending. The baseline data is created for each wheel independently, and it associates commanded torque to reaction wheel speed. The tool compares the measured data from the spacecraft with the baseline, producing a set of residuals that we call delta torque. These values are passed through a Kalman filter and the resulting trend line is studied to find changes in behavior. We have identified torque changes that occurred in the two failed wheels before they were lost completely. Since the start of K2, our tool has also identified friction events in the remaining two reaction wheels. This tool was developed specifically for the Kepler mission, but the method could be easily applied to any mission that uses reaction wheels.
I. Introduction
The Kepler mission was launched in 2009 on a 3.5-year prime mission to discover Earth-like planets around distant stars. Kepler’s instrument is a photometer to measure light intensity, and its original target was a region of sky near the Cygnus and Lyra constellations which is dense with stars and can be observed continuously throughout the year [1]. As planetary bodies transit in front of their host stars, the photometer measures changes in stellar intensity caused by these transits, and through repeated measurements we can use this method to find planets around stars outside of our own solar system. These bodies are termed exoplanets, and since launch Kepler has discovered 2,343 confirmed exoplanets, 2,244 candidate exoplanets, and 30 Earth-like exoplanets in the habitable zone [2].
In April 2012, NASA approved an extension of the Kepler mission through fiscal year 2016, giving the spacecraft additional time to complete its scientific goals [3]. In July of the same year, the Kepler spacecraft experienced an anomaly when reaction wheel assembly 2 (RWA2) stopped spinning and remained at 0 rpm. Kepler was launched with four wheels, and with only three wheels, it was possible to continue the Kepler mission despite the failure of RWA2. Rather than spend time and resources troubleshooting the operation of RWA2, a decision was made to turn off the anomalous wheel, allowing science data collection to continue on the three remaining healthy wheels [4]. However, the return to science was relatively short-lived—after a period of increased friction, reaction wheel assembly 4 (RWA4) also experienced a permanent critical failure, suspending science data collection until a solution could be found or the mission declared over. Fortunately, the imaginative engineers working on Kepler developed a new operations concept and pointing strategy to minimize the amount of attitude error, and complementary scientific targets were identified so the mission could continue [4–7]. This pointing strategy reoriented the vehicle to reduce, but not eliminate, the effect of torque from solar radiation pressure while relying heavily on the remaining two wheels and Kepler’s reaction control system to minimize attitude error drift around the boresight of the telescope. What followed was a continued and renewed effort to monitor the health of the remaining two wheels such that any change in behavior would be seen in advance, as it was with RWA4.
∗Command Controller, Mission Operations & Data Systems, 1234 Innovation Drive, Boulder, CO 80303. AIAA Student Member. †Mission Operations Manager, 1600 Commerce Street, Boulder, CO, 80301. AIAA Senior Member.
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Downloaded by 134.122.89.123 on March 29, 2021 | http://arc.aiaa.org | DOI: 10.2514/6.2018-2563
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II. Background
A. Concept of Operations for the Attitude Determination and Control System (ADCS)
As this mission has evolved, so too has the ADCS concept of operations. The general concept is the same—take science data continuously for weeks to months, then once data collection is complete, maneuver the vehicle so the high gain antenna can point at Earth to downlink the data. During both Kepler and K2, the spacecraft uses two main science attitude pointing modes, called Fine Point and Coarse Point. For science collection, Fine Point is the desired state since this is when the pointing is most finely controlled and produces the best science data. If the spacecraft cannot maintain this pointing in science attitude, it will briefly regress to Coarse Point until it can regain fine pointing control. When not taking science, the spacecraft will usually maneuver into its downlink configuration, though occasionally an anomaly will force Kepler into a different attitude configuration.
K2 wheel operations are unusual compared to other missions—rather than allowing the wheels to spin up from a low speed while maintaining the spacecraft attitude, the wheels begin a period of operation at a high speed, then the speed slowly decreases as the solar radiation pressure bleeds momentum from the spacecraft. Every two days, the wheels are spun back up in a wheel resaturation maneuver. The wheels never cross into the sub-elastohydrodynamic (sub-EHD) zone below 300 rpm unless they are unused in favor of a thruster-controlled attitude. A side-by-side comparison of Kepler and K2 nominal data for RWA1 is presented in Fig. 1.
Fig. 1 Nominal wheel speed profile of Reaction Wheel 1 for science collection, shown for both Kepler data (left) and K2 data (right). Both plots span an 88 day period. During the Kepler mission, the wheels were often operated closer to the sub-EHD zone below 300 rpm, and wheel desaturations occurred every 3 days. In K2, the wheels are spun in the opposite direction, at higher speeds, and wheel resaturations occur every 2 days. In the Kepler data, the jumps in speed correspond to monthly contacts where the spacecraft executed a maneuver.
B. Reaction Wheels and Failure Modes
Reaction wheel failures have unfortunately become an expected anomaly in the business of operating spacecraft, with a checkered history of single or multiple failures on programs such as the Hubble Space Telescope, Dawn, Cassini, FUSE, the Solar Dynamics Observatory (SDO), and Hayabusa in addition to others that have been less well-documented [8–13]. In a 2005 paper by A. Marua, et al., the authors note that reaction wheels fail for a variety of reasons, including increases in wheel motor current, increases in friction of the wheel, a bus voltage failure while the wheel is at high speed, or simultaneous smaller magnitude increases in motor current and friction [14]. A recent study [15] by engineers William Bialke and Eric Hansell at United Technologies Corporation suggests a root cause of many reaction wheel failures, discussing a potential correlation between reaction wheel friction events and the space environment. The authors show that coronal mass ejection events can alter the charge of a spacecraft, causing arcing and damage within the reaction wheel assembly. Other sources of reaction wheel failure are lubrication starvation, operation in the sub-EHD zone, and lubricant build-up [10, 16].
Regardless of the eventual root cause, we know that increases in friction can lead to decreased wheel performance
and potentially wheel failure. While we can’t measure friction in the system directly, we can compare the wheel speed that we expect to be produced for a given torque commanded to the motor. This is a known technique for monitoring reaction wheel friction—in the 2014 paper by K. A. Larson, et al., the authors discuss their most powerful method for monitoring Kepler’s wheel health: "The figure of merit that was most used to evaluate wheel health was plotting the reaction wheel torque command versus speed to pick out any deviations from the normal trend. In healthy wheels, the amount of torque command needed to spin a wheel at a given speed is predictable" [4]. Similarly, the Solar Dynamics Observatory uses speed vs. torque analysis to study the health of their wheels, finding that "[t]rending of the RWA telemetry as a function of wheel speed and/or commanded torque...proved useful during the initial telemetry review for differentiating between non-nominal values and those to be expected based on pre-launch data and on-orbit experience" [13]. Reaction wheel manufacturers also use the speed vs. torque method, specifically Goodrich/Ithaco stated that "it served as one of their primary methods for assessing bearing friction changes in on-orbit wheels" [13]. Considering the history of the failures with RWA2 and RWA4 and the availability of speed and torque data, using this technique has become our primary method for monitoring the wheels for changes in behavior. As we discuss later, we have expanded this technique to use a baseline set of data and a filter that allows us to more closely monitor changes in wheel behavior. C. The Role of LASP and the Command Controllers
Throughout the transition from Kepler to K2, monitoring the reaction wheels was always a critically important task, but over time the reach expanded to the mission operations student employees at the Laboratory for Atmospheric and Space Physics (LASP), part of the University of Colorado Boulder (CU). In the hierarchy of the Kepler mission, LASP serves as the Mission Operations Center, and the students at LASP work as Command Controllers where they are certified to conduct real-time operations for the Kepler, MMS, SORCE, AIM, and QuikSCAT missions. Additionally, the students analyze engineering telemetry on a daily, weekly, monthly, and quarterly basis, support anomaly recovery efforts, and develop software tools to monitor spacecraft health and safety. The undergraduate and graduate student authors of this paper worked on Kepler’s attitude determination and control system (ADCS) team for the past 3 years, and in that time have developed analysis tools to characterize the health and performance of Kepler’s reaction wheels. This work supports and supplements the critical work of LASP’s partners at Ball Aerospace & Technologies Corporation which serves as the Flight Planning Center, and NASA’s Ames Research Center. The student’s work serves as both a learning opportunity and an additional verification of the work of professional engineers.
Since the Command Controllers at LASP monitor Kepler/K2 mission telemetry on a regular basis, there is a consistent effort to ensure that the data we are looking at is worthwhile. For example, it may be useful to monitor the temperature of the reaction wheel motor since deviations can be seen easily in the raw data, but simply looking at wheel speeds does not give insight into the performance of the reaction wheel as a whole. The Solar Dynamics Observatory faced a similar challenge, noting that time-averaging their reaction wheel data helped with "discerning trends that were not immediately clear to the naked eye in short-term plots of the raw data" [13]. The challenge facing the students is how to extract the relevant information from all this data—our solution is discussed in detail in Section III.
D. Failure of RWA2 and RWA4
The first reaction wheel to fail on Kepler was RWA2, which went from healthy to failure so quickly that no intervention was possible operationally. After the spacecraft was recovered and operated successfully on three wheels, RWA4 began to show increased friction and ultimately experienced a critical failure as well. Fig. 2 shows the engineering data from the time of each failure, with RWA2 on the left from July 2012 and RWA4 on the right from May 2013.
From the telemetry, we know that in both cases the commanded torque values became quite noisy and the wheel speeds also showed a departure from the usual pattern. While the data on its own is interesting and is important for understanding the wheel failures, it can be difficult to appreciate how the friction in the wheel changed just before and during the anomalies. Analysis of these failures with our tool will be shown in Section IV.
Fig. 2 Wheel speed and commanded torque raw telemetry for RWA2 and RWA4 just before, during, and after their failures. After failure, both wheels remained at 0 rpm despite efforts to recover the wheels.
III. Methodology
A. Delta Torque as a Performance Monitor
Fig. 3 Speed vs. commanded torque re-lationship for RWA1, for nominal K2 data. There is generally a linear relationship be-tween wheel speed and commanded torque, but it is a coarse estimation of the behavior. We have expanded the traditional torque vs. speed tool to expand
our capabilities in wheel performance analysis. By focusing on the residuals of the data as compared with a baseline set of data, we can more easily see changes in wheel performance. One of the underlying assumptions of this analysis is that the relationship between torque and speed should be consistent. In an idealized system, a particular commanded torque value would consistently cause the motor to produce the same wheel speed, and we could back-predict the torque based on a measured wheel speed. In reality we know that this relationship isn’t perfect, and establishing a baseline set of data that represents a wheel’s typical behavior allows us to know that we are representing true behavior as best as possible.
Fig. 3 shows a set of nominal speed vs. commanded torque data for RWA1, with a least-squares line of best fit added to show the relationship between these two measures. While the line does represent the overall trend between the two variables, it does not capture behavior near the extremes of the wheel speeds since the data is less consistent. Because this is a coarse estimation of the wheel behavior, we decided to explore another method of establishing a norm that would better demonstrate the true behavior of each reaction wheel at different speeds.
Instead of fitting a line to this data, we have created a set of baseline data for Kepler and K2 that correlates each wheel speed to a
torque value. This baseline data is assembled from engineering telemetry during periods of stable pointing in Fine Point lock, and analyzed to ensure that it is an appropriate "truth" data set to compare to. A detailed description of this process is included in section III.B. Once the baseline is established, we can compare any set of data to the baseline to
identify changes in wheel behavior. In other words, how much does the data deviate from the norm? Rather than relying on visual deviations from the line as shown in Fig. 3, we plot the residuals from baseline and expect the trend to stay clustered around zero. We call these residuals delta torque because they refer to the change or delta of the measured torque from the expected baseline torque.
1. Friction and a Statistical Filter
Delta torque describes the friction present in the system, and to compute this value we subtract the data we’re interested in analyzing from the expected torque for a given speed. An unintended complexity arises due to the way Kepler reports wheel telemetry. The wheel can spin in both directions, but one direction produces positive speed and torque, while the other direction produces negative speed and torque. As you can see in the equations below, these two cases that must be considered differently. This distinction is made so that increases in the magnitude of the torque are correctly identified as increases in friction, and decreases in the magnitude of torque are correctly identified as decreases in friction. Similarly, we exclude any values where the signs contradict, i.e. a positive wheel speed that has a negative torque value associated with it. This analysis uses commanded torque rather than measured torque, these instances only occur when the wheel is accelerating significantly on purpose. This is not considered nominal data for the purposes of comparing with a baseline.
For positive wheel speeds and torques: ∆τ = τmeas−τbaseline For negative wheel speeds and torques: ∆τ = − (τmeas−τbaseline)
(1) If a positive delta torque value is obtained, this indicates more friction than expected. If a negative delta torque value is obtained, this indicates less friction than expected for that wheel speed. In an idealized system, the delta torque would simply be a flat line at zero, but in reality our system is more complex. Low resolution of the reaction wheel speed adds complexity to this analysis—we only see speeds binned discretely every 8 or 9 rpm while the commanded torque values have much more resolution. This means we will see some variation in the delta torque trend as the wheel speed moves between resolved values.
Fig. 4 Nominal delta torque with filtered signal for RWA1, data taken from Campaign 11 of K2.
Fig. 5 Nominal delta torque with filtered signal for RWA3, data taken from Campaign 11 of K2.
To alleviate variation introduced by the wheel speed resolution and the noise in the commanded torque, we employ a statistical filter. The purpose of the filter is to further reduce the noise and highlight trends that are difficult to see otherwise. The plot of delta torque with filtered signal is the final product of the analysis, although we will also look at the filtered signal on its own. We use these plots to identify trends that require further analysis or simply as a way to monitor the long-term health of a reaction wheel. Figs. 4 and 5 show a set of nominal data from Campaign 11 of K2 with the filtered line shown in red.
Some information can be gleaned from the delta torque itself, notably that envelope of deviation grows over time. Since the spacecraft attitude stays the same for approximately 3 months at a time during K2, the wheels spin down
faster over time to maintain spacecraft pointing. This increase in wheel spin down is caused by the angle between the incoming solar radiation pressure and the spacecraft’s unbalanced axis. Over the course of a K2 campaign, the angle changes, and SRP exerts more force on Kepler. However, we can see that the filtered line is stable with a small magnitude and is not influenced by the widening envelope. Even if the envelope is getting larger the overall performance is in family with the baseline data.
2. Verification of Delta Torque as an Analysis Tool
Since this tool was first developed in 2015, we have had 3 years of verification showing that it can identify changes in wheel behavior that are difficult to see from raw telemetry. As will be discussed in Section IV, we can use other engineering telemetry to support the hypothesis that the changes represent physical behavior in the reaction wheels, though there is no way to prove this definitively. We have observed that reaction wheel performance has declined incrementally as the wheels have continued to age. The more noteworthy development is when we see abrupt changes or trends that affect a particular region of wheel speed or commanded torque, as will be shown in Section IV. As long as the trends are consistent and slow-changing we can infer that the wheels have typical performance for their age, though this is also difficult to prove definitively. This is why the statistical filter is essential to our tool—despite the data envelope changing over time, the filter allows us to see a consistent trend line, essentially pulling a friction signal from the raw data.
One caveat for this method is that we only receive full-resolution engineering data about every 3 months at the end of each campaign, and this tool is dependent on having a full set of data in order to work. We primarily use this tool to analyze past data to see how the wheels have changed in the last three months rather than trying to see changes during a campaign immediately after they happen. For missions that receive data more frequently, this tool could be used to see changes soon after they occur, which may help operators make real-time decisions about wheel operation.
B. Developing a Performance Baseline
The delta torque method requires a set of data to act as truth data to make a proper performance comparison. Current trends are compared against the baseline data which is a measurement of true performance. Based on the known failure modes, the critical metric is the commanded torque needed to produce a particular wheel speed. The baseline data provides a known relationship between wheel speed and commanded torque, but determining how to develop this baseline can be challenging.
Truth data for reaction wheel torque and speed can be developed from a variety of places, and selecting a good source of data is important. Theoretical models are available that attempt to provide a torque value for a given reaction wheel speed, taking into account various types of friction [17, 18]. Although these methods are valuable in predicting overall reaction wheel performance, for our purposes there are more accurate and realistic sources of comparison data for our individual wheels. Test data from pre-launch activities is another source of comparison but does not match the true environment of the actual wheels. For mission operators, the most available and accurate source of comparison data is engineering telemetry downlinked directly from the spacecraft. This data is taken in the environment where the performance needs to be evaluated, while performing mission functions. For our tool we use reaction wheel speed directly measured by the hardware and the commanded motor torque from the attitude controller. This is the best possible source of data on the nominal performance of the reaction wheels.
1. Turning Telemetry into a Baseline
The construction of a baseline data set consists of choosing specific time periods where reaction wheel behavior is thought to be nominal. This should consist of screening these time periods for general attitude performance and spacecraft performance. For the original Kepler mission we chose data once Kepler began its nominal science mission, just after a period of commissioning and preliminary science observation. At this time Kepler was using the wheels in a manner consistent with the rest of the prime mission. The wheels had a small amount of use, indicating that any early burn out or degradation in the wheels was no longer a concern. In addition, the wheels were brand new and did not yet have the wear and tear of many years of science observations.
The construction of the K2 baseline data set was slightly more complicated. Once again we chose a set of data after the initial tests and preliminary observations, but we found that we did not cover a wide enough range of wheel speeds. In fact, no K2 campaign gave us the full range of wheel speeds we needed for our analysis. In particular, the Campaign 7 and 15 data that we used for a baseline did not reach the extremities of wheel speeds above 4700 rpm and below
2700 rpm. In order to have a baseline data set outside of these ranges we added a portion of the wheel speed data from Campaign 3 and Campaign 9, allowing us to have data above 4700 rpm and below 2700 rpm. This stitching gave us a complete set of wheel speeds for K2. Although there is likely a performance degradation in the later campaigns that was not present in Campaign 7, based on the resulting plots it does not appear to be an issue. Adding additional data acts to make our baseline more conservative by including more variable behavior from each campaign. Additionally, Kepler’s orbit is eccentric enough to cause seasonal variations in thermal and power behavior as the spacecraft’s distance to the sun grows and shrinks over the course of its orbit. By combining campaigns, we’ve added this variable to the baseline as well, which makes our baseline data more conservative for the purpose of comparing campaigns.
With a good set of raw telemetry to work with, we need to convert this time series data to a baseline set. The data is processed by removing time stamps and sorting the wheel speed and its related commanded torque by wheel speed. On Kepler wheel speeds are resolved in specific integer values as measured by the sensors on the spacecraft. During nominal operations the wheels spin between 300 and 700 discrete speeds depending on the mission segment and the reaction wheel. These differences in the number of discrete wheel speeds stem from the fact that Kepler had a smaller range of wheel speeds compared to K2. For each discrete wheel speed, the commanded torques associated with that wheel speed are grouped together and averaged, resulting in a single torque value. The end product of the baseline creation is a simple table that correlates wheel speed to expected commanded torque. A sample of this process is shown in Table 1, which uses a small selection of data to illustrate the process.
Table 1 These tables show a sample of how the baseline data set is created. From left to right, we take the raw Fine Point lock data for a particular wheel and mission segment and sort it by wheel speed. The torques associated with each wheel speed are averaged and a new table is created that associates a single torque value with a single wheel speed.
Unsorted Data Speed [rpm] Torque [mN·m] 3015 21.0418 3007 19.7459 3007 19.8454 3007 20.0201 3015 20.9150 3015 19.1016 3007 19.8338 3015 19.4349 3015 18.9457 3007 19.6199 .. . ...
→
Sorted by Wheel Speed Speed [rpm] Torque [mN·m] 3007 19.8338 3007 19.7459 3007 19.6199 3007 19.8454 3007 20.0201 3015 20.9150 3015 21.0418 3015 19.1016 3015 19.4349 3015 18.9457 .. . ...
i
i
Averaged Torques Speed [rpm] Torque [mN·m] 3007 19.8130 3015 19.8878 .. . ...In general, the relationship between wheel speed and commanded torque is non-linear, though early in the mission it followed an expected monotonically increasing trend. Figure 6 shows our baseline data of commanded torque versus speed for all four reaction wheels. There is a discontinuity in the baseline data at 0 rpm when the commanded torque transitions from negative to positive values. The discontinuity is expected because there is a minimum torque required to overcome the static friction to begin rotating the wheel from a standstill. The average slope between the four wheels is 6.05 × 10−3mN·m/rpm and the four wheels have little vertical offset in commanded torque. Early in the mission the wheel behavior was consistent between each wheel.
As the reaction wheel assemblies age and experience increased wear, non-linear effects can be introduced, and we have seen this clearly in RWA1 as the mission has continued. In K2, RWA1 has shown a predictable non-linear step-like shape at high speeds starting at 3600 rpm and becoming more pronounced above 4200 rpm. Figure 7 shows the behavior for RWA1 and RWA3 for K2, which clearly illustrates the non-linear behavior of RWA1. Since this behavior is unique to this particular wheel, our customized baseline data allows us to account for non-linear behavior without compromising the analysis.
The non-linear behavior is expected at this point in the mission, using actual data from the spacecraft allows us to
remove these idiosyncrasies that are not concerning for the overall health of the wheel. This step like behavior has been present in all of K2 and is not related to the stitching process we used to cover the full range of wheel speeds.
If we didn’t create a baseline data set, we would likely fit a curve to the data and extrapolate a torque for a given wheel speed. Fitted curves inherently introduce some error, and would be considerably different than the linear behavior seen in RWA1 during K2. From our experience with this method using data sourced from the spacecraft leads to less noise in the final plots and an enhanced ability to see changes in behavior.
Fig. 6 Baseline data sets for the Kepler segment of the mission, showing linear trends with an average slope of 6.05 × 10−3mN·m for each 1 rpm of wheel speed. Note the discontinuity in the baseline data at 0 rpm where the commanded torque transitions from negative to positive values.
Fig. 7 Baseline data sets for the K2 segment of the mission, showing linear trends with an average slope of 4.26 × 10−3mN·m for each 1 rpm of wheel speed. The behavior of RWA1 at high speeds becomes non-linear and varies in a step-like fashion, while RWA3 experiences smaller non-linearities at high speeds.
2. Issues to Consider in Constructing the Baseline Data
We consider several issues before choosing time ranges for telemetry when constructing the baseline data set. The activities performed on-orbit and the attitude configuration need to be considered, since we don’t want to use data where we expect unusual behavior. We have data from the entire mission with a few gaps due to anomalies, but not all data is consistent with expected wheel trending. From launch to the end of 2017, the spacecraft was in Fine Point lock for approximately 87.7% of the time, which as discussed previously is the primary science observation attitude. The remaining data is from when the wheels are not used to control the attitude or the spacecraft attitude changed. We only use data when the spacecraft was in Fine Point lock since we have an abundance of data to choose from, and our goal is to trend reaction wheel performance during science collection.
Configuration changes should also be considered and avoided if possible. The most obvious change is the difference between original Kepler and K2. The attitude and operations are entirely different in the two mission segments, and we had to create completely separate baseline data sets to accommodate. Configurations in the ADCS controller have changed since launch, including parameters that affect the reaction wheels and thrusters. Gain updates were made to the reaction wheels after K2 Campaign 2, so a new baseline was developed. We did not want to use data prior to Campaign 2 for a baseline of the rest of K2 as these gain updates could effect the relation of commanded torque and wheel speed.
One challenge we faced after a baseline time range was identified is the resolution of the raw wheel speed data. The downlinked wheel speed has a resolution of approximately 8 to 9 rpm, which is coarser than we would like for this analysis. Fortunately, in Kepler and K2 the reaction wheels speed moves over a range between 3000 to 4500 rpm for nominal operations. With this large range even a coarse speed resolution has been sufficient to perform this analysis. Additionally, the range of torque values is small, and only varies slightly from one wheel speed to another. About 98% of values for a given wheel speed are less than 0.30 mN·m different, and even if we had finer wheel speeds the analysis would be largely the same.
The consistency of the resolution in wheel speed we receive on the ground needs to be addressed as well. Luckily on Kepler there is a fixed set of wheel speeds that we receive in telemetry. The way the data is created on the spacecraft, we will never receive a wheel speed where no speed has been previously recorded. We are able to construct a baseline data set that correlates a single wheel speed to an averaged torque value. Furthermore, the commanded torque and wheel speed are downlinked in the same telemetry packet. The result is that the wheel speed and torque data have matching time stamps and a matching cadence. The measurement alignment simplifies our analysis by allowing a 1:1 sampling rate of wheel speed and commanded torque. Missions that do not measure wheel speed and torque at the same time and cadence would have to devise a method of matching wheel speed measurements and torque values. Linear interpolation could perform this matching, but would then cause issues with irregular wheel speeds that fall between possible measurements.
The last issue to consider in constructing the baseline data is the reaction wheel thermal profiles. There is a perceived relationship between reaction wheel friction and temperature observed over many Kepler quarterlies and K2 campaigns. It is important to make sure that the thermal profile of the baseline data matches a similar thermal profile for the analyzed data. The Kepler spacecraft experiences a small and consistent thermal change in the wheels over the course of a science campaign, and even this small trend is visible in the final delta torque plots. We are also aware that the thermal profile of the spacecraft changes over the course of its orbit due to the change in solar distance from orbital eccentricity. These changes do effect the baseline data, and it is important to be aware of their impacts on long term changes in delta torque. C. Creation of a Statistical Filter
The creation of a statistical filter was the final step to process the data, and allows trends in friction to become visible. While the unfiltered delta torque metric is valid for very large increases or decreases in torque, it does not detect the subtle events that we are interested in.
1. The Kalman Filter
Since the commanded torque data that we receive from the spacecraft is the result of a noisy electrical signal, it was natural to consider using a Kalman filter to provide an estimate of the commanded torque to reduce some of the noise. We don’t have a dynamical model to use since we are working with actual data, so instead we consider our system to be the measured delta torque data that is produced from Eq. 1. This system has one degree of freedom, which is the discrete time-ordered delta torque. This single degree of freedom allows us treat the covariance matrices for process and measurement noise as scalars, denoted as Q and R respectively. By tuning Q and R we can affect the output of the filter by essentially increasing or decreasing the amount of noise that is allowed to pass through. The values we chose for Q
and R are relatively subjective—we chose them based on a visual inspection of the output, and tried to strike a balance between a readable signal and one that wasn’t severely filtered as to remove features of the data.
We model the dynamics of the system as a first order Gauss-Markov process, which we are able to use because our system satisfies the assumptions for this type of process. One requirement is that the system have a finite number of possible values; since delta torque is derived from a physical system with hardware limitations, the values cannot become infinitely large or small, and therefore the delta torque is finite. Another assumption we satisfy is that future values are dependent on past values, which again is evident because we have a physical system that cannot randomly jump between values. Additionally, we assume that the probability distribution of noise in the delta torque is constant over the time scales used for analysis, and that these probabilities are normally distributed [19, 20]. Our data conforms to these assumptions, and allows us to use the Gauss-Markov model.
Upon application of the filter, the noise of the delta torque is reduced and we arrive at a better estimation of what the signal looks like. Throughout this paper, all of the filtered data that is shown has been accomplished with this method unless stated otherwise. Fig. 8 shows three plots that highlight the conversion from raw delta torque to filtered data—on the left is the raw delta torque for a period of nominal data from RWA1, the middle plot shows the data with the Kalman filter applied in red, and on the right is the filtered line on its own with a different y-axis scaling. This data is nominal, and as such the filtered line does not tell us anything interesting about the delta torque overall. However, in Section IV we will present instances where this tool and filter have identified changes in behavior.
Fig. 8 These three figures show the conversion from raw delta torque to filtered data for a period of nominal data for RWA1. On the left is the raw delta torque data, the middle shows the Kalman filter applied in red, and the plot on the right shows the filtered line by itself with a more appropriate y-axis scaling.
2. Moving Average Filter
While using a Kalman filter is the preferred method, it is possible to still gain valuable information about the delta torque by using a simple moving average. In order to demonstrate these calculations, the same RWA1 data as shown for the Kalman filter was taken from January 18th, 2017 to January 22nd, 2017. In Fig. 9, the plot on the left shows the raw delta torque metric; clearly this data is noisy and if any trends are present, they are hidden inside the noise. In order to smooth the data set, we experimented with two variations on a moving average filter. The middle plot in Fig. 9 shows that a 3-point moving average filter does indeed remove some noise but further clarity of the long term trend is desired. To further reduce the noise, we employed a 25-point moving average filter, shown on the right in Fig. 9, which resulted in an interesting plot that showed more features of the data. Of course, by increasing the number of points used by the moving average there is a cost, in that some information is lost by smoothing more points at one time. The moving average filters used here take an equal number of points from before and after the data element being processed, and the initial and final elements are not manipulated in any way.
Fig. 9 These three figures show the conversion from raw delta torque to filtered data using a moving average filter. On the left is the raw delta torque data, the middle shows a 3-point moving average line in red, and on the right we show a 25-point moving average line, also in red.
We experimented with reducing the data before filtering or averaging. In one trial, we tried a process that removed data beyond six standard deviations of the mean to essentially remove outliers before filtering. Ultimately we decided that any kind of data trimming could cover up useful trends, particularly since we don’t know how the data will change in the future. Since the moving average smoothing process is essentially a low pass filter, there is a risk of cutting off high frequency trends with this process, which is one disadvantage of this method. The team also experimented with various weighting methods in addition to the moving average, but ultimately decided that this standard averaging technique is a good secondary option if a Kalman filter cannot be implemented.
IV. Results
A. Changes Before RWA2 Failure
It was natural during the development of this tool that we looked back to the earlier wheel failures before K2. We were all quite surprised that we could see several short-term significant events of increased friction leading up to the first failure, and that there was also a subtle change in the delta torque trend that persisted for approximately six months before the ultimate failure of RWA2. We do want to temper this statement and note that this tool does not necessarily show a causal effect between a change in delta torque and wheel failure. It is unlikely that you could predict an impending failure due to only a change in delta torque. Even if this tool was developed earlier, the knowledge of these events would not have allowed the Kepler engineers and operators to do anything additional to predict or prevent a failure. However, these changes are noteworthy given the whole picture of a reaction wheel’s health, and detecting changes in delta torque behavior may be grounds for further investigation.
Fig. 10 shows the filtered delta torque for RWA2 from June 17, 2009 up to the failure of RWA2 on July 16th, 2012. June 17, 2009 was chosen as a start time because it coincided with the start of a main science quarter which occurred shortly after the start of the prime mission. The filtered delta torque in Fig. 10 tells a new and intriguing story of RWA2. Throughout the prime mission and before changes in trending, the filtered delta torque of RWA2 oscillated around zero mN·m. These oscillations near 1 have a period of about 3 months, which correlates with the periodic maneuvers to reorient the spacecraft each quarter during the original Kepler mission. After each quarter, the vehicle’s attitude was changed to keep the solar panels pointed at the Sun while keeping the boresight of the telescope pointed at the same region of the sky. As shown in Fig. 11, at the start of a quarter RWA2 had less direct sunlight hitting the wheel housing, and then over the next three months the housing would slowly warm up with increased sunlight. Fig. 11 is the same time period as Fig. 10, and we can conclude the 3-month oscillatory period of the filtered delta torque is correlated with the thermal trending of the overall spacecraft, and is therefore not concerning in terms of friction events. The roughly year long oscillatory trend in reaction wheel temperatures is due to the changes in solar distance from the orbit’s eccentricity. This trend does not appear in Fig. 10, but it is important to be aware that it could have been present in that plot.
Fig. 10 Filtered delta torque from start of prime mission to RWA2 failure, with annotations for notable events. 1 shows nominal delta torque trending for original Kepler observation periods. 2 shows an unrelated safe mode event. 3 , 4 , 5 , and 6 show large increases in delta torque that were documented in the post-failure investigation. 7 shows the ultimate failure of RWA2.
Fig. 11 Housing temperature for RWA2, showing the quarterly and seasonal thermal trends that oc-cur on the spacecraft. This thermal trending can explain some of the changes in friction that we see in RWA2 since the start of prime mission.
The presence of large increases of delta torque over short timescales such as at points 3 , 4 , 5 , and 6 was documented in the post-failure investigation of RWA2. This spiking behavior is visible even in the unfiltered delta torque, which we do not show here. This large scale spiking was determined to be an early sign of failure in RWA2, and was used to anticipate the failure of RWA4.
The other interesting trend of note is that about 6 months before the eventual failure of RWA2, there is a significant change in the baseline delta torque on this plot. After the larger torque spikes labeled 4 , the baseline torque value increased by about 1 m·Nm, a small but significant value. This indicates that after the torque spike at 4 occurred there was a long lasting change in performance of the wheel. Without delta torque this change in trending would be difficult to identify.
The final failure of the wheel was characterized by a second increase in the baseline delta torque just a few weeks before the failure. This secondary increase is visible at 6 in the plot. Finally, on July 16th, 2012 RWA2 finally failed. Fig. 10 shows the delta torque during the failure at point 7 . The delta
commanded torque spiked to over 15 mN·m. The commanded torque reached a maximum value and vehicle fault protection took action to move into Coarse Point. Although later attempts were made to recover the wheel, the wheel did not respond and was removed permanently from the attitude control system.
B. RWA4 Failure
Fig. 12 Filtered delta torque for RWA4 from the start of three-wheel operations through the failure of RWA4. As discussed previously, the failure of RWA2 spurred a three-wheel operations concept, and once this mode was established, the spacecraft was able to continue nominal science operations. Fig. 12 shows the filtered delta torque starting from when the three-wheel control concept was established and stopping when RWA4 ultimately failed. Several points are highlighted on the plot to help tell the story of RWA4’s eventual failure.
From the start of the plot to point 1 , the trending is nominally flat and near zero. Although the torque does increase significantly near 1 , this does align with thermal changes to RWA2 so it is difficult to discern whether this change is due to thermal trending or an increase in friction. More interestingly at 2 , the delta torque shows a sudden increase from the downward trending present before, indicative a small increase in friction. Point 3 is when the wheels were off due to a safe mode event that was unrelated to the reaction wheels. The delta torque shows another small increase near 4 , but once again this appears to be well-correlated to expected reaction wheel thermal trending. Although there were several small events in the first half of three wheel control operations, the overall trending was nominal.
In January of 2013, the nominal trending changed dramatically as shown at 5 , with an increase of approximately 2 mN·m. Since the failure of RWA2, the commanded torque was being monitored closely, and this increase was immediately caught in the raw commanded torque telemetry. To try and recover from this friction, a 10-day wheel rest activity was planned. This activity took the spacecraft out of Fine Point and commanded the wheels to 0 rpm, resulting in a zero value for the delta torque during this activity, marked at point 6 . After the wheel rest was complete, the wheels showed slightly lower delta torque for approximately 8 days before increasing to larger values than before the wheel rest activity. The wheel continued to show large spikes of friction increases in addition to a higher baseline delta torque, until its eventual failure on May 12, 2013. Unlike the failure of RWA2, there were fewer changes in trending leading up to the failure that could be identified, though it is interesting to see this failure through a new lens.
At this point in the mission, the wheels were under a great deal of scrutiny, and our tool does not show any new trending before the failure of RWA4. This is a testament to the engineers that worked the Kepler wheel anomalies. Our tool does provide a valuable and easily visible way to see the trending of these wheels compared to their expected baseline values.
C. Catching the K2 Campaign 12 RWA1 Disturbance
As mission operators we regularly review and trend telemetry, including our filtered delta torque. While preparing for one of our regular telemetry review sessions, we noticed that there was a small deviation in delta torque for RWA1 during Kepler’s previous science campaign. Figs. 13 and 14 show the deviation which we found during our standard review process at 1 . Note that 2 is a data gap due to an unrelated safe mode event.
Fig. 13 Fig. 14
When we first saw this deviation we were slightly confused. Typically we expect to see reaction wheel friction increase, as this is a known failure mode on many other spacecraft. We were surprised then to see the friction decrease. Although we knew it could be an actual decrease in the torque on the spacecraft, we were concerned that our tool had incorrectly identified a deviation from normal RWA1 behavior.
At this point, we decided that this event required more investigation, and a double check on the validity of our tool. The deviation lasted approximately 12 hours, and occurred just after a wheel resaturation. To confirm this event, we needed to eliminate any issues with attitude errors, unexpected wheel speeds, or thruster issues. Not finding any issues with these parameters, we further investigated the commanded torque on RWA1 during the disturbance. Fig. 15 shows the raw commanded torque from the spacecraft during the time period of the deviation, and it is clear that you cannot see any abnormal trending. While the raw torque is noisy and will momentarily spike during resaturations as shown, this is a familiar trend and not unusual. Since we could not conclude anything from the raw data, our next step was to analyze the pre-disturbance and post-disturbance resaturation periods for a more direct comparison of the data.
Fig. 15 Raw commanded torque data for RWA1 show-ing the resaturation periods before, durshow-ing, and after the disturbance. It is difficult to see anything unusual about this data, all three periods look the same at first glance.
We expect the slope of the commanded torque data to be fairly consistent for adjacent resaturation periods, though over a full campaign the slope will change. We expect that the resaturation periods surrounding the dis-turbance would have a similar trend even though they are from different time periods a few days apart. Fig. 16 shows the raw torque data for three resaturation periods— before, during, and after the disturbance. Fig. 17 shows the same resaturation periods, except the data has been filtered using the same Kalman filter that we apply in our delta torque tool. Although there appears to be very little difference when looking at the unfiltered plot, the filtered plot shows that the commanded torque during the disturbance is different. Without this filter and the comparison, it is unlikely that we would have detected a this change.
This comparison and filter are the key aspects of the delta torque that make it such and effective tool. Our method combines this comparison and filter into a single plot that can be easily evaluated. After all of this analysis, we were able to determine that there had been a momentary change in the performance of RWA1. For all the plots and work we had done, we still did not have a good answer on why this event occurred. We were reassured that the event appeared to only take place for a 12 hour period, and that the delta torque indicated the rest of the science campaign
took place without any other disturbances or changes in delta torque. We still do not know why this disturbance occurred,
but it is not visible in the raw data and only our tool has been able to pick up on this disturbance.
Fig. 16 Resaturation periods of raw commanded torque for RWA1 overplotted, showing that from the raw telemetry it is unlikely that any difference would be detected between the three resaturations.
Fig. 17 The same data as Fig. 16, but filtered; suddenly it is possible to see that the resaturation period with the disturbance has a different trend from the resaturation periods before and after.
V. Applications
Our main goal with this paper is to provide a new method to detect changes in reaction wheel performance that may not be visible in raw data. Our hope is that we can inspire other mission operators to implement similar methods on their spacecraft. In order to do so, we provide a few words of caution and advice when implementing this method. First and foremost, we only use this tool for analysis once we have a full set of data. Kepler downlinks the full engineering set of data once every 80 days, and between these large downlinks we may only receive a handful of data points. With so little data, the statistical filter does not have enough data to properly remove noise, and the context of the data is reduced. Due to these issues, we only trend Kepler’s delta torque once the full data set has been downlinked. For missions that receive data at more frequent opportunities, this analysis could be performed more often.
Another important consideration is that this method is really only meant to provide an indication that the performance of the reaction wheel has changed. Although a close analysis could likely pull additional information from the delta torque plots when correlated with other telemetry, delta torque itself is focused on changes in wheel performance.
A secondary goal of this analysis is simplicity—the delta torque method is essentially centered around a single subtraction, a comparison of actual to expected. Even though we use a Kalman filter to provide a better estimate of the delta torque signal, other filters could also work to produce similar results. As we showed, even a simple moving average can remove most of the unwanted noise that clouds the true behavior. This performance metric can be quickly and easily implemented for use in regular performance monitoring or real-time analysis.
This tool is could also be useful for relating increases in reaction wheel torque events to solar weather phenomenon. As Bialke and Hansell described in their 2017 paper, Kepler’s reaction wheels may have failed due to solar coronal mass ejection events that caused spacecraft charging and electrical discharges within the wheels [15]. Our tool could be combined with space weather predictions to help correlate friction events with these solar storms. Fig. 10 shows the extreme changes in friction that were mentioned in Bialke and Hansell’s paper, as well as more subtle changes before the failure of RWA2 occurred.
VI. Conclusion
Our goal with this delta torque tool was to provide a novel way of monitoring the performance of reaction wheels with respect to their friction. Increases in reaction wheel friction is a major cause of reaction wheel failures, and after two reaction wheel failures on the Kepler spacecraft, we developed our tool to monitor the remaining healthy wheels.
We were also able to validate our tool using the previous failures and several years’ worth of use. The delta torque plots distinctly showed the failures of both wheels, but interestingly also showed early changes in trending that were not observed before the wheel failures.
Although our tool is able to pull out changes in trending, it is not able to point to a cause of reaction wheel failures. This is perhaps the weakest point of our tool—its inability to provide context to a change in reaction wheel performance. Yet it still finds a worthy purpose in making small changes in trending visible and easily identifiable. Further context and explanation is left to the mission operators and system engineers. We sincerely hope that others may find value in this tool as well, and encourage interested readers to contact any of the authors with further questions.
Acknowledgements
The authors would like to extend their sincerest thanks to Kipp Larson from Ball Aerospace and Lee Reedy from LASP for their invaluable guidance, mentorship, and feedback as we worked on this project. We cannot overstate how important this project has been to our growth as engineers and problem-solvers, and we wouldn’t have been nearly as successful without their support. Additionally, the authors would like to thank Katelynn McCalmont-Everton and Huikang Ma, former students that laid the groundwork for the original development of this tool, Sean Ryan from LASP, who provided valuable feedback on our paper, and Matt Muszynski, who provided extremely helpful input in the development of our filter. Lastly, the authors wish to thank their colleagues at LASP and Ball for their endless encouragement, camaraderie, and laughter.
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