Techniques for characterizing turbomachinery blade motion and related systems and methods

Abstract

Techniques are described for measuring and characterizing the behavior of turbomachinery using radio frequency sensors. The characterization of the turbomachinery produced by the techniques described herein may, for instance, improve engine design processes and / or allow for real-time and / or in-flight monitoring of engines. According to some embodiments, the techniques described herein comprise arranging a plurality of radio frequency antennas proximate to a rotating portion of an engine, such as a shaft coupled to a plurality of rotor blades. In some embodiments, the radio frequency antennas may be placed around a cavity formed by a housing, such as a compression cavity or a turbine cavity in a jet engine.

Description

TECHNIQUES FOR CHARACTERIZING TURBOMACHINERY BLADE MOTION AND RELATED SYSTEMS AND METHODSCROSS-REFERENCE TO RELATED APPLICATIONS

[0001] The present application claims the benefit under 35 U.S.C. § 119(e) of U.S. Provisional Patent Application No. 63 / 563,735, filed March 11, 2024, titled “Radio Frequency Sensors to Characterize Turbomachinery Blade Vibration,” which is hereby incorporated by reference in its entirety.GOVERNMENT FUNDING

[0002] This invention was made with government support under grant N00014-22- 1-2495 awarded by the Office of Naval Research (ONR). The government has certain rights in the invention.BACKGROUND

[0003] Rotating machinery, such as turbomachinery, is susceptible to degradation and breakdown over its operating lifetime. Typically, maintenance is conducted on a schedule, which means that some machinery are inspected unnecessarily while others are not repaired until after failure. Alternatively, maintenance can be condition-based, where the machinery is monitored for indications of decreasing performance or malfunctions. Maintenance is then performed based on the machinery health information. In some cases, machinery may be monitored to compare performance to desired operating conditions during the design process, rather than during active operation.SUMMARY

[0004] According to some aspects, the techniques described herein relate to an apparatus including: a housing including a shaft coupled to a plurality of rotor blades; a plurality of radio frequency (RF) antennas arranged within the housing, the plurality of RF antennas including a first RF antenna and a second RF antenna; and at least one processor configured to: operate the first RF antenna to transmit a first RF tone; operate the second RF antenna to receive a signal while the first RF antenna transmits the firstRF tone; generate a frequency spectrum for a portion of the signal received during a first time period; and determine a rotational speed of the plurality of rotor blades during the first time period based on the frequency spectrum.

[0005] According to some aspects, the techniques described herein relate to a method including: operating a first radio frequency (RF) antenna arranged within a housing to transmit a first RF tone, wherein the housing includes a shaft coupled to a plurality of rotor blades; operating a second RF antenna to receive a signal while the first RF antenna transmits the first RF tone; generating, using at least one processor, a frequency spectrum for a portion of the signal received during a first time period; and determining, using the at least one processor, a rotational speed of the plurality of rotor blades during the first time period based on the frequency spectrum.

[0006] The foregoing apparatus and method embodiments may be implemented with any suitable combination of aspects, features, and acts described above or in further detail below. These and other aspects, embodiments, and features of the present teachings can be more fully understood from the following description in conjunction with the accompanying drawings.BRIEF DESCRIPTION OF DRAWINGS

[0007] Various aspects and embodiments will be described with reference to the following figures. It should be appreciated that the figures are not necessarily drawn to scale. In the drawings, each identical or nearly identical component that is illustrated in various figures is represented by a like numeral. For purposes of clarity, not every component may be labeled in every drawing.

[0008] FIG. 1 depicts a cross-sectional view of an illustrative apparatus in which aspects of the present disclosure may be practiced, according to some embodiments;

[0009] FIG. 2 depicts an illustrative example of a frequency spectrum of such tones in an embodiment in which four RF transmitters are operating, according to some embodiments;

[0010] FIG. 3 is a flowchart of a method of estimating a rotational speed of a shaft of an engine, according to some embodiments;

[0011] FIG. 4 depicts an illustrative example of harmonic responses, according to some embodiments;

[0012] FIG. 5 is a flowchart of a method of identifying synchronous and / or asynchronous vibrations in a shaft of an engine, according to some embodiments;

[0013] FIG. 6 depicts an illustrative order spectrum, according to some embodiments;

[0014] FIG. 7 depicts illustrative asynchronous vibrations present in an order spectrum, according to some embodiments;

[0015] FIG. 8 is a flowchart of a method of tracking the rotational position of a shaft of an engine, according to some embodiments;

[0016] FIG. 9 depicts relative polarization energy of measured polarization components of a received RF signal over a number of rotations, according to some embodiments;

[0017] FIG. 10 depicts a change in polarization response over time, according to some embodiments;

[0018] FIG. 11 is a flowchart of a method of identifying vibrations or other undesirable behavior in a shaft of an engine, according to some embodiments;

[0019] FIGs. 12A-12B depict polarization state changes over time on Poincare spheres, according to some embodiments;

[0020] FIG. 13 depicts a polarization state change over time for a given shaft angle, according to some embodiments;

[0021] FIG. 14 depicts Doppler measurements of rotor blades, according to some embodiments;

[0022] FIG. 15 depicts an illustrative engine, according to some embodiments; and

[0023] FIG. 16 illustrates an example of a computing system environment on which aspects of the disclosure may be implemented.DETAILED DESCRIPTION

[0024] Rotating machinery such as gas turbine engines, rotor blades and stator airfoils are subject to constant but potentially unsteady forces that can lead to unwanted vibrations. In some cases, these vibrations can be large enough to be catastrophic for the machinery. While measurement of these vibrations is possible, this is generally limited to specialized ground-based testing or component rigs. This limits the ability to characterize vibrations both in-flight and in real-time.

[0025] The present disclosure relates to techniques for measuring and characterizing the behavior of turbomachinery using radio frequency sensors. The characterization of the turbomachinery produced by the techniques described herein may, for instance, improve engine design processes and / or allow for real-time and / or in-flight monitoring of engines.

[0026] According to some embodiments, the techniques described herein comprise arranging a plurality of radio frequency (RF) antennas proximate to a rotating portion of an engine, such as a shaft coupled to a plurality of rotor blades. In some embodiments, the RF antennas may be placed around a cavity formed by a housing, such as a compression cavity or a turbine cavity in a jet engine. For example, each RF antenna may be embedded in the housing or arranged in an opening (e.g., a portal) in the housing of the cavity. The RF antennas may be arranged so that there is no material between each antenna and the rotor blades as they move, or at least no material that would interfere with RF signals (e.g., metal). In addition, the RF antennas may be placed around the cavity so that signals from some of the RF antennas pass through the blade envelope (the volume of space carved out by motion of the rotor blades) when the signal propagates from one RF antenna to another.

[0027] As described further below, RF signals that are transmitted through a cavity from an RF antenna may be incident on spinning rotor blades in the cavity before being received by another of the RF antennas, and the received signal may thereby contain information on the position of one or more of the rotor blades. For instance, a signal transmitted by one of the RF antennas will typically reflect off fixed and dynamic scattering surfaces, and some of the energy of the transmitted signal will couple into one or more RF antennas being operated to receive RF signals.

[0028] Various analysis techniques, described herein, may be applied to signals received by one or more of the RF antennas to characterize aspects of the rotor blade’s motion and / or motion of the shaft to which the rotor blades are coupled. For instance, one or more signals may be analyzed to determine a rotational rate of the rotor blades, which may change over time, indicating vibrations or other undesirable behavior. Other aspects that may be identified from the signal(s) may include rotor whirl, a single problematic blade of the rotor blades, and the ability to track the rotational angle of the rotor blades over time.

[0029] According to some embodiments, an RF antenna may be operated to transmit an RF tone that is received by another RF antenna located across a cavity from the transmitting RF antenna. An RF tone may refer to an RF signal that is in principle transmitted at a single carrier frequency, and may also be referred to herein simply as a “tone.” For instance, an RF tone may be transmitted at a primary carrier frequency while also containing frequency components that deviate within a small range (e.g., 500 kHz or less) from the primary frequency. By transmitting RF tones at different, non-overlapping carrier frequencies, multiple signals may be transmitted at the same time among the RF antennas yet the receiving RF antennas can determine which of the RF antennas transmitted different portions of the received signals. That is, the transmitted RF signals may be orthogonal to one another in frequency space. As a result, the number of signal paths is equal to the number of RF antennas transmitting multiplied by the number of RF antennas receiving. Each of these signal paths may be modulated by surfaces within the cavity and can be interpreted to characterize any dynamics within the apparatus, potentially providing a lot of information on the dynamics of the rotor blades and shaft. In some embodiments, one or more RF antennas may be operated to continuously transmit their RF tone(s) during a sensing operation.

[0030] To more clearly explain the operation of the various RF antennas, in some cases an RF antenna may be referred to herein as an RF transmitter or an RF receiver. It will be understood that these terms refer to the manner of operating an RF antenna and are not intended to imply that there is a necessarily a structural difference between an RF antenna being operated as an RF transmitter and an RF antenna being operated as an RF receiver (although such differences may in some cases be present). As such, references to RF transmitters or RF receivers will be understood to refer to the manner in which RF antennas are operated rather than necessarily being indicative of a difference in their physical structure.

[0031] Following below are more detailed descriptions of various concepts related to, and embodiments of, techniques for measuring and characterizing the behavior of turbomachinery using radio frequency sensors. It should be appreciated that various aspects described herein may be implemented in any of numerous ways. Examples of specific implementations are provided herein for illustrative purposes only. In addition,the various aspects described in the embodiments below may be used alone or in any combination, and are not limited to the combinations explicitly described herein.

[0032] FIG. 1 depicts a cross-sectional view of an illustrative apparatus in which aspects of the present disclosure may be practiced, according to some embodiments. In the example of FIG. 1, apparatus 100 comprises a housing 101 that forms a cavity in which a turbomachinery device is arranged and which includes a shaft 110 and rotor blades 112 (of which two are labeled). RF antennas 121, 122, 123 and 124 are arranged within the housing and each may be configured to transmit and / or receive RF signals. As described above, a signal from an RF transmitter will typically reflect off fixed and dynamic scattering surfaces within an engine such as that shown in FIG. 1 , and some of the energy of the transmitted signal will couple into one or more RF receivers. While in principal any of the RF antennas 121, 122, 123 and 124 may be operated as RF transmitters or RF receivers, in the example of FIG. 1 the RF antennas 121 and 122 are depicted as RF transmitters and the RF antennas 123 and 124 are depicted as RF receivers. RF antennas may be arranged in various positions within a housing, and as illustrative examples the RF antennas 121 and 123 are shown as being arranged within a recessed portion of the housing 101, whereas RF antennas 122 and 124 are shown as being arranged within a portal through the housing.

[0033] According to some embodiments, the cross-sectional view of apparatus 100 represents part of a turbomachinery system, such as a cross-sectional view through a compression chamber or a turbine chamber. The shaft 110 and rotor blades 112 may therefore, for example, be part of a compressor or a turbine, and may form part of a low- pressure or high-pressure portion of a system. For example, the cross-sectional view shown in FIG. 1 may represent any suitable cross-section through the illustrative engine shown in FIG. 15.

[0034] In the example of FIG. 1, the RF transmitters 121, 122, 123 and 124 are coupled to a processor 150. The processor 150 may include any suitable computing device, including any suitable combination of hardware and software, and is configured to operate the RF transmitters 121, 122, 123 and 124 and analyze signals received by RF receivers to measure and characterize the behavior of the turbomachinery represented by shaft 110 and rotor blades 112 via the techniques described herein. The processor 150 may be wirelessly coupled and / or wired to any one or more of the RF transmitters 121 ,122, 123 and 124 and configured to send and receive data to / from such RF transmitters to perform operations such as transmitting a signal from an RF transmitter and receiving signal data from an RF receiver.

[0035] According to some embodiments, the RF antennas 121, 122, 123 and 124 may each be a polarized antenna, such as a dual-polarized antenna (e.g., a dual-polarized reciprocal circular waveguide). As such each of the RF antennas 121, 122, 123 and 124 may, when transmitting, be configured to transmit a polarized RF signal (e.g., a circular polarized or elliptical polarized RF signal). Similarly, when receiving, each RF antenna may be configured to receive a polarized RF signal (e.g., a circular polarized or elliptical polarized RF signal) and produce signals that characterize the polarized RF signal (e.g., in-phase / quadrature (I / Q) signals). In some embodiments, signals produced by the RF receivers 123 and 124 in response to received RF signals (e.g., I / Q signals) may be sent from the respective RF receiver to the processor 150 for analysis.

[0036] In some embodiments, the resonant frequency of each of the RF antennas 121, 122, 123 and 124 is greater than or equal to 10 GHz, 12.5 GHz, 15 GHz, 17.5 GHz, 20 GHz, or 22.5 GHz. In some embodiments, the resonant frequency of each of the RF antennas 121, 122, 123 and 124 is less than or equal to 25 GHz, 22.5 GHz, 20 GHz, 17.5 GHz, 15 GHz, or 12.5 GHz. Any suitable combinations of the above-referenced ranges are also possible (e.g., the resonant frequency of each of the RF antennas 121, 122, 123 and 124 is greater or equal to 15 GHz and less than or equal to 20 GHz, etc.).

[0037] While the RF transmitters 121 and 122 are depicted in the example of FIG.1 as being on one side of the cavity while the RF receivers 123 and 124 are on the opposing side of the cavity, RF transmitters and receivers may be in general be placed in any suitable location relative to one another, and in any number. For instance, in some embodiments a single RF transmitter and multiple RF receivers may be employed, or vice versa, and in any relative locations. Similarly, the processor 150 may send and receive data to any number of RF transmitters and RF receivers via the techniques described herein.

[0038] As described above, in some embodiments an RF transmitter may be configured to produce one or more RF tones, each being transmitted at a single principal frequency. Moreover, where multiple RF transmitters are transmitting RF tones, the frequencies of the RF tones may be selected to be non-overlapping (orthogonal) so thatan RF receiver can identify which RF transmitter transmitted a received RF tone of a particular frequency. FIG. 2 depicts an illustrative example of a frequency spectrum of such tones in an embodiment in which four RF transmitters are operating, according to some embodiments.

[0039] In the example of FIG. 2, a composite frequency spectrum of nine RF tones is depicted with the line shading indicating which of four RF transmitters is transmitting in which portion of the spectrum. In particular, RF tones 201a, 201b and 201c are, in the example of FIG. 2, emitted by a first RF transmitter; RF tones 202a and 202b are emitted by a second RF transmitter; RF tones 203a and 203b are emitted by a third RF transmitter; and RF tones 204a and 204b are emitted by a fourth RF transmitter. Each RF transmitter may in general transmit any number of RF tones, and the relative frequency arrangement of RF tones from multiple RF transmitters need not be arranged in a sequential arrangement as shown in FIG. 2.

[0040] FIG. 3 is a flowchart of a method of estimating a rotational speed of a shaft of an engine, according to some embodiments. Method 300 may be performed by any suitable processor, including but not limited to processor 150 shown in the example of FIG. 1.

[0041] Method 300 begins with receiving an RF signal in act 302. Act 302 may comprise an RF receiver receiving an RF signal that comprises one or more RF tones at different frequencies as described above. The RF signal may comprise RF tones transmitted by any number of RF transmitters, including one, two, three or four RF transmitters, with each RF transmitter transmitting any number of RF tones, including one, two, three or four RF tones. For instance, the RF signal received in act 302 may comprise sixteen RF tones at different frequencies, where each of four RF transmitters transmitted four of the sixteen RF tones at different frequencies.

[0042] Act 302 may comprise receiving an RF signal with a polarized antenna, and consequently multiple signals may be produced in response to receiving the RF signal in act 302. For instance, act 302 may comprise producing 1 / Q signals from an RF receiver in response to receiving an RF signal, as described above.

[0043] In act 304, the processor performing method 300 generates one or more frequency spectra for each of a number of time periods. According to the some of thetechniques described herein, the frequency spectrum of a given received RF tone during a short time period may be determined. Such a frequency spectrum may be determined repeatedly for successive time periods to generate data that indicates the frequency / energy relationship of the received RF signal over time. Time periods for such an analysis may be a fraction of the rotation rate of the shaft (e.g., shaft 110 in the apparatus of FIG. 1). For instance, a typical shaft may rotate once in between 1 ms and 100 ms, such as between 1.5 ms and 10 ms (i.e., corresponding to 40,000 RPM and 6,000 RPM, respectively), depending on the rotation rate. As such, the time window chosen for the analysis in act 304 may be around 1 ps, such as between 1 ps and 5 ps, in length. Alternatively, time-domain filtering can be applied that preserves the original sample rate (for example 50 MHz) without use of a time windowed operation (such as a Short Time Fourier Transform).

[0044] In some embodiments, a frequency spectrum generated in act 304 may be generated in the following way. First, a received signal may be down-converted in frequency to translate each of the RF tone frequencies present in the received signal to a baseband signal centered at the zero frequency. For example, a Hilbert transformation may be applied to the RF signal. Second, a low-pass filter may be applied to each translated RF tone signal. The frequency bandwidth of the low-pass filter may be selected based on the anticipated harmonic frequencies of the shaft and rotor blades that are present in the received RF signal. After filtering, the frequency spectrum for a given RF tone frequency may be generated. According to some embodiments, window sizes to process the down-converted (and filtered) tone sequence may either fixed in terms of the number of samples; can be variable so that the number of samples is selected to approximately correspond to an integer multiple of the shaft rotation period; or the sequences may be uniformly sampled in rotation angle (which requires a time-to-angle domain transformation). Alternatively, the first and second steps above (the downconversion and filtering) may be reversed, i.e., the RF tone frequencies are filtered with a bandpass filter and then the filtered signal is down-converted to a baseband signal (e.g., using a Hilbert transformation).

[0045] In some embodiments, signals of interest are embedded in the time-domain modulations induced from the environment on the RF tones. The tones can be isolated in at least one of two ways: down-conversion with filtering and a Fast Fourier Transform(FFT)-based approach such as STFT. A frequency spectrum may be generated in act 304 by applying a short time Fourier transform (STFT) to the received RF signal, or signals derived therefrom. An STFT performed in this way produces a time sequence of spectra that includes the RF tones, and from which time-domain sequences for each of the modulated RF tones can be extracted. The modulations correspond to frequency content from the shaft rate and associated harmonics and vibrations. Similarly, the downconversion and low-pass filtering approach produces a time-domain series for the down- converted tone that includes frequency content from the shaft and associated harmonics and vibrations. This approach may be applied for each RF tone of interest. In some embodiments, an anti-aliasing filter is applied to the RF signal, or signals derived therefrom, prior to performing the STFT (e.g., filters around each known RF tone frequency to limit the frequency content to the RF tones).

[0046] From the time-series associated with each RF tone (recall that in some cases there may be multiple RF tones for each pair of RF transmitters and RF receivers), a STFT or similar processing may be applied to the RF tone sequence to elicit frequency content of the modulated tone as a function of time. Tn act 306, the frequency spectra (e.g., from the STFT of the tone sequences) are analyzed to determine a blade pass frequency. The inventors have found that the blade pass response is typically a strong signal in the generated frequency spectra, and exhibits multiple harmonics that retain relatively high signal to noise ratios. An illustrative example of harmonic responses is shown in FIG. 4.

[0047] In the example of FIG. 4, illustrative data derived from a plurality of frequency spectra generated from STFTs of a plurality of tones are depicted, with vertical slices of the depicted data representing frequency spectra from respective instants in time, arranged contiguously side by side to produce an indication of how the energy in certain frequencies changes over time in a received RF signal. As may be seen from FIG. 4, multiple blade pass harmonics of a fundamental frequency response are visible (the patterns are repeated at multiple different frequencies).

[0048] According to some embodiments, act 306 may comprise identifying a plurality of energy peaks in one or more frequency spectra generated in act 304 (e.g., by the STFT of tone data), which correspond to harmonics of the blade pass frequency. The frequency at which a relatively strong energy peak appears indicates a blade passfrequency, or a harmonic of the blade pass frequency. Any of these harmonics may be analyzed to determine the frequency of the blade pass, although there may be a benefit to analyzing the highest frequency harmonic that does not exhibit aliasing to measure a frequency of the energy peak. In particular, high frequency harmonics may exhibit very little interference from other signals, and consequently the frequency measurement may be more easily determined when looking to a high frequency harmonic of the blade pass frequency than a lower frequency harmonic of the blade pass frequency. In any case, when the frequency of a blade pass harmonic’s energy peak is determined in act 306, this frequency is divided by the harmonic number to determine the actual blade pass frequency. For instance, the lowest frequency blade pass signal may be identified and the harmonic number determined based on the relative scaling of the frequencies of the signal and the higher harmonic signal.

[0049] In act 308, the processor performing method 300 determines the rotational speed of the shaft based on the blade pass frequency determined in act 306. For instance, where the rotor blades are evenly spaced around the shaft, the rotational frequency of the shaft may be determined by dividing the blade pass frequency by the number of rotor blades. The rotational speed (e.g., revolutions per minute (RPM)) may then be determined from the shaft’s rotational frequency.

[0050] Act 306 and 308 may in some cases be performed multiple times for different RF tones to generate a more accurate determination of the blade pass frequency and / or shaft rotational frequency. For instance, multiple determinations may be made and the mean of these determinations calculated.

[0051] FIG. 5 is a flowchart of a method of identifying synchronous and / or asynchronous vibrations in a shaft of an engine, according to some embodiments. Method 500 may be performed by any suitable processor, including but not limited to processor 150 shown in the example of FIG. 1.

[0052] In act 502, the processor performing method 500 determines a rotational speed of a shaft (e.g., shaft 110 in FIG. 1) from a received RF signal. For instance, act 502 may comprise performing part or all of method 300 to determine the rotational speed of the shaft in act 308.

[0053] In act 504, the processor performing method 500 generates one or more revolution-matched frequency spectra for each of one or more time periods. In the example of FIG. 3, because the rotational rate of the blades may in general vary over time (e.g., as seen by the changing vertical position of the energy peaks in FIG. 4), the time window over which each frequency spectrum was generated in act 304 is not necessarily duration-matched to the rotational rate. That is, in method 300 the time windows may have a fixed duration. In contrast, in act 504 the time window over which each frequency spectrum is determined is based on the rotational speed of the shaft determined in act 502. For example, the time window size for an STFT operation performed on an RF signal may be selected dynamically for successive time windows based on the estimated rotational shaft speed at that time (e.g., using a time window size corresponding to an integer number of rotations of the rotor blades). This process produces a plurality of frequency spectra over time, as shown in FIG. 6, which exhibit reduced spectral leakage and which concentrate energy into appropriate discretized bins to provide a cleaner representation of the underlying phenomena

[0054] In the example of FIG. 6, as with FIG. 4, vertical slices of the depicted data represent single frequency spectra, which are arranged side by side to produce an indication of how the energy in certain frequencies changes over time in a received RF signal. However, since the frequency spectra are generated based on the determined rotational shaft speed for each corresponding time window, the harmonics are comparatively horizontal. These harmonics, also referred to herein as “orders” represent the shaft harmonics with some finite spread in frequency. The spectra depicted in FIG. 6 may also be referred to herein as an “order spectrum.”

[0055] According to some embodiments, an order spectrum may be generated in act 504 by performing a plurality of STFTs on an RF signal, or a signal derived therefrom, wherein the time window size for each STFT is selected based on a determined shaft rotational speed / frequency at a time corresponding to the time window (e.g., the time at the start of the time window). An STFT performed in this way produces a time sequence of spectra for each of the frequencies corresponding to the RF tone frequencies, effectively generating a plurality of frequency spectra for each of a number of time periods with durations keyed to the rotational speed / frequency of the shaft.

[0056] Method 500 also includes act 506 and 508, either or both of which may be performed to identify synchronous or asynchronous vibration modes, respectively, from the order spectrum generated in act 504.

[0057] In act 506, the processor performing method 500 identifies one or more synchronous vibrations by identifying a change in energy of one or more of the orders of the order spectrum when the shaft rotational frequency is at a particular value. For example, the order spectrum shown in FIG. 6 depicts an example of data that was gathered while the rotational speed of a shaft was gradually increased over time. As seen at time 610, a spike in the relative energy in each orders was generated when the rotational speed hit a particular speed. By determining the rotational speed of the shaft when such an increase in energy of one or more orders occurred, synchronous vibrations of the shaft at this frequency can be identified. This may allow the engine designer to, for instance, avoid operating the engine at this speed.

[0058] In act 508, the processor performing method 500 analyzes the order spectrum generated in act 504 to identify vibration modes, such as torsion, flex or bend modes, within the order spectrum. In some embodiments, the shaft harmonics (orders) in the order spectrum may be subtracted from the order spectrum to leave a spectrum of other modes that might be present in the orders. A frequency spectrum for a particular time may then be analyzed to identify any asynchronous modes that were present in the original order spectrum.

[0059] As one example, FIG. 7 depicts a frequency cut of an order spectrum (e.g., a vertical slice through the order spectrum shown in FIG. 6). The shaft harmonics have been subtracted in this example, and leave a mixture of several modes (which in this example include nodal diameters with flex and torsion vibrations), four of which are identified as shown. The various peaks of multiple asynchronous modes mixed together may for instance be identified through a technique such as singular value decomposition (SVD). In some embodiments, once shaft harmonic modes have been identified, these modes may be subtracted in a transform domain, such as a uniformly sampled angle domain.

[0060] FIG. 8 is a flowchart of a method of tracking the rotational position of a shaft of an engine, according to some embodiments. Method 800 may be performed byany suitable processor, including but not limited to processor 150 shown in the example of FIG. 1.

[0061] In act 802, the processor performing method 800 measures a polarization response of a received RF signal. In some embodiments, act 802 comprises determining multiple polarization components of the received RF signal, such as with a polarization mode dispersion (PMD) analysis. In act 804, the polarization response is resampled using a time window selected based on the observed angular change of the polarization response measured in act 802. Similar to the order spectrum described above, which determines the sampling window duration dynamically based on the rotational speed of the shaft, in the example of method 800 the sampling window is determined dynamically in act 804 based on the angular change in the polarization response.

[0062] In act 806, the sampling in act 804 is arranged to produce an estimate of the angular position of the shaft over time. That is, the data produced in act 804 shows how polarization changes as a function of shaft angle, which allows the shaft angle to be tracked over time (which may also be referred to herein as “theta tracking”).

[0063] FIG. 9 depicts an example of the data produced in act 804, wherein the relative polarization magnitude of measured polarization components of a received RF signal is depicted for a given shaft angle over a number of rotations. The periodic vertical bands represent the same blades passing by over and over again in successive rotations, and the bands across the range of shaft angles represent the different rotor blades that pass in a single rotation of the shaft. The angle of a given RF tone as a function of shaft angle and rotation number may also be determined as an alternative to relative energy, providing a similar response.

[0064] Tracking the shaft angle over time allows for various improved estimates to be made, including an improved shaft rotation rate determination, which may be determined in act 808 by numerically differentiating the angular position vector of the polarization response to obtain an angular velocity as a function of time.

[0065] In addition, subtracting the data of successive rotations from the next rotation to leave only the changes in the responses across each rotation may allow detection of various behaviors. As shown in FIG. 10, for instance, subtracting the mean of the relative energy from the data shown in FIG. 9 does not produce a uniform data set,indicating that the behavior of the shaft and / or rotor blades for later rotations were different than for earlier rotations (the relative magnitude of the data shown in FIG. 10 has been exaggerated for clarity).

[0066] FIG. 11 is a flowchart of a method of identifying vibrations or other undesirable behavior in a shaft of an engine, according to some embodiments. Method 1100 may be performed by any suitable processor, including but not limited to processor 150 shown in the example of FIG. 1.

[0067] In act 1102, the processor performing method 1100 characterizes the polarization state between multiple RF transmitter and RF receiver pairs. For instance, a single RF transmitter may transmit an RF signal that is received by each of two orthogonally-polarized RF receivers. The relative polarization response observed across the two RF receivers may be characterized for a given RF tone frequency, such that a number of characterizations may be obtained and independently used for subsequent steps in method 1100. In some embodiments, act 1102 comprises determining a Stokes vector (e.g., a 4-element Stokes vector) to characterize polarization. In the case that the RF receivers correspond to spatially separated antennas, similar representations may be used, but are not technically Stokes polarization parameters since the receiver pair is not comprised of orthogonally polarized antenna ports with a common phase center. Unique Stokes vectors, in this more general sense, may be computed for each pair of received signals associated with a chosen transmit signal.

[0068] In act 1104, irrespective of how the polarization state between RF transmitter / receiver pairs is characterized, the processor performing method 1100 identifies a cycle of the changing polarization state for one or more rotor blades. For instance, the polarization state data describing a given rotor blade may be expected to be periodic in some manner. In some cases, each rotor blade may exhibit similar periodic changes in its polarization state. FIGs. 12A and 12B depicts an example of periodic states that may be observed in the polarization state characterized in act 1102, with FIG. 12A depicting the periodic path through the Poincare sphere for a single rotor blade, and FIG. 12B depicting the periodic path through the Poincare sphere for multiple rotor blades in an engine. A characterization of polarization determined in act 1102 based on Stokes values can, for instance, be represented by the Poincare sphere as shown in FIGs. 12A and 12B. In some embodiments, act 1 104 comprises determining how thepolarization state changes over time for a given shaft angle. The shaft angle may be determined, for instance, as described above in relation to FIG. 8.

[0069] In act 1106, the processor performing method 1100 identifies vibrations, a malfunctioning rotor blade and / or rotor whirl based on the polarization state data generated in act 1102 and analyzed in act 1104. In embodiments in which act 1104 comprises identifying a periodic state change of multiple rotor blades (e.g., a periodic path through the Poincare sphere), deviations from a collective periodic state change may indicate some kind of malfunction or other undesirable behavior. For instance, using the Poincare representation for purposes of illustration, if one of the paths for a given rotor blade deviates from the paths for the other rotor blades, this could indicate that the deviating blade has developed a fault. Similarly, if the path through the Poincare sphere for all blades drifts between cycles (e.g., the first cycle for the rotor blades exhibits a different path than subsequent cycles for the rotor blades), this could indicate rotor whirl. Such issues may thereby be identified based on analysis of the polarization state data for one rotor blade or for a group of rotor blades.

[0070] In embodiments in which act 1104 comprises determining how the polarization state changes over time for a given shaft angle, vibrations may be detected by determining that the polarization state for that shaft angle has changed over time. For instance, FIG. 13 depicts polarization state data at a given shaft angle for a single blade over time (i.e., one data point is produced during each rotation of the shaft). The Poincare sphere shows polarization state measurements for successive rotations of the shaft at that shaft angle, which is also depicted in the data at the left and right which show the two angles of the polarization state in the sphere. The bottom data depicts the energy of the polarization state over time. As may be seen from the data in FIG. 13, the polarization state changes noticeably at a particular time identified in the drawing with a dashed line. For instance, the energy drops and the noise in the polarization state angles increases at around this time. This may for example indicate that vibrations began at that time. Therefore, by determining how the polarization state (e.g., angles, energy) changes over time for a given shaft angle, changes in behavior such as vibration may be detected.

[0071] In some embodiments, an analysis technique for characterizing rotor blade motion includes performing Doppler measurements of the blades, where the Doppler energy provides an indication of blade deflection. In particular, a suitable processor(e.g., processor 150 in FIG. 1) may determine a change in frequency between a transmitted RF tone and a received RF tone. By using a suitably small time window and frequency window, the variation in received energy as a function of frequency over time may be measured. An illustrative example of Doppler measurements in this manner is shown in FIG. 14, according to some embodiments.

[0072] It will be appreciated that the above-described techniques for analyzing RF signals may be combined in any suitable combination to provide a range of insights into a single received signal. In addition, any of these techniques may be repeated for multiple RF tones present in a single RF signal. By combining multiple RF transmitters and RF receivers that are transmitting and receiving multiple RF tones, the methods described above may for instance be performed many times for a given time period through performance of the methods for multiple RF tones for a given RF receiver and for multiple RF receivers.

[0073] In some embodiments, an expected blade pass time may be determined by tracking the angle position of one or more rotor blades and / or the rotational speed of the shaft. This expected blade pass time may be compared with an actual, measured blade pass time to produce a differential time measurement. This determination may be made for successive shaft rotations to determine how the differential time measurement changes over time, which may allow for further characterization of the vibration deflection of one or more blades.

[0074] An illustrative implementation of a computer system 1600 that may be used to control an RF transmitter, an RF receiver and / or analyze RF signals to perform any of the techniques described above is shown in FIG. 16. For instance, the computer system 1600 may represent part or all of processor 150 shown in FIG. 1. The computer system 1600 may include one or more processors 1610 and one or more non-transitory computer-readable storage media (e.g., memory 1620 and one or more non-volatile storage media 1630). The one or more processors 1610 may control writing data to and reading data from the memory 1620 and the one or more non-volatile storage media 1630 in any suitable manner, as the aspects of the disclosure described herein are not limited in this respect. To perform functionality and / or techniques described herein, the one or more processors 1610 may execute one or more instructions stored in one or more computer-readable storage media (e.g., the memory 1620, storage media, etc.), whichmay serve as non-transitory computer-readable storage media storing instructions for execution by the one or more processors 1610.

[0075] In connection with techniques described herein, code used to, for example, control an RF transmitter, an RF receiver and / or analyze RF signals, etc. may be stored on one or more computer-readable storage media of computer system 1600. The one or more processors 1610 may execute any such code to perform any of the above-described techniques as described herein. Any other software, programs or instructions described herein may also be stored and executed by computer system 1600. It will be appreciated that computer code may be applied to any aspects of methods and techniques described herein. For example, computer code may be applied to perform a short time Fourier transform of a signal, etc.

[0076] The various methods or processes outlined herein may be coded as software that is executable on one or more processors that employ any one of a variety of operating systems or platforms. Additionally, such software may be written using any of numerous suitable programming languages and / or programming or scripting tools, and also may be compiled as executable machine language code or intermediate code that is executed on a virtual machine or a suitable framework.

[0077] In this respect, various inventive concepts may be embodied as at least one non-transitory computer readable storage medium (e.g., a computer memory, one or more floppy discs, compact discs, optical discs, magnetic tapes, flash memories, circuit configurations in Field Programmable Gate Arrays or other semiconductor devices, etc.) encoded with one or more programs that, when executed on one or more computers or other processors, implement the various embodiments of the present disclosure. The non- transitory computer-readable medium or media may be transportable, such that the program or programs stored thereon may be loaded onto any computer resource to implement various aspects of the present disclosure as described above.

[0078] The terms “program,” “software,” and / or “application” are used herein in a generic sense to refer to any type of computer code or set of computer-executable instructions that can be employed to program a computer or other processor to implement various aspects of embodiments as described above. Additionally, it should be appreciated that according to one aspect, one or more computer programs that when executed perform methods of the present disclosure need not reside on a single computeror processor, but may be distributed in a modular fashion among different computers or processors to implement various aspects of the present disclosure.

[0079] Computer-executable instructions may be in many forms, such as program modules, executed by one or more computers or other devices. Generally, program modules include routines, programs, objects, components, data structures, etc. that perform particular tasks or implement particular abstract data types. Typically, the functionality of the program modules may be combined or distributed as desired in various embodiments.

[0080] Also, data structures may be stored in non-transitory computer-readable storage media in any suitable form. Data structures may have fields that are related through location in the data structure. Such relationships may likewise be achieved by assigning storage for the fields with locations in a non-transitory computer-readable medium that convey relationship between the fields. However, any suitable mechanism may be used to establish relationships among information in fields of a data structure, including through the use of pointers, tags or other mechanisms that establish relationships among data elements.

[0081] Having thus described several aspects of at least one embodiment of this disclosure, it is to be appreciated that various alterations, modifications, and improvements will readily occur to those skilled in the art. For instance, aspects of the techniques described herein may be combined in any of the following ways:

[0082] Example 1. An apparatus comprising: a housing comprising a shaft coupled to a plurality of rotor blades; a plurality of radio frequency (RF) antennas arranged within the housing, the plurality of RF antennas including a first RF antenna and a second RF antenna; and at least one processor configured to: operate the first RF antenna to transmit a first RF tone; operate the second RF antenna to receive a signal while the first RF antenna transmits the first RF tone; generate a frequency spectrum for a portion of the signal received during a first time period; and determine a rotational speed of the plurality of rotor blades during the first time period based on the frequency spectrum.

[0083] Example 2. The apparatus of example 1, wherein the at least one processor is further configured to determine a frequency of at least one vibration of the shaft and / or vibration of one or more of the plurality of rotor blades.

[0084] Example 3. The apparatus of example 1, wherein the housing comprising a plurality of openings and wherein the first RF antenna and the second RF antenna are each arranged in respective openings in the housing.

[0085] Example 4. The apparatus of example 1, wherein the plurality of RF antennas are dual-polarized RF antennas.

[0086] Example 5. The apparatus of example 1, wherein the at least one processor is configured to operate the first RF antenna to transmit a plurality of RF tones at different frequencies.

[0087] Example 6. The apparatus of example 1, wherein the at least one processor is configured to identify a blade pass frequency based on the frequency spectrum for the portion of the signal, and to determine the rotational speed of the plurality of rotor blades based on blade pass frequency.

[0088] Example 7. The apparatus of example 6, wherein the at least one processor is configured to: identify a plurality of energy peaks in the frequency spectrum for the portion of the signal, the plurality of energy peaks corresponding to harmonics of the blade pass frequency; and identify the blade pass frequency by identifying a frequency of the lowest frequency harmonic of the plurality of energy peaks.

[0089] Example 8. The apparatus of example 1, wherein the at least one processor is configured to generate a plurality of frequency spectra each corresponding to a respective time period of a plurality of time periods over which the signal was received by the second RF antenna, and wherein the rotational speed of the plurality of rotor blades is determined based on the plurality of frequency spectra.

[0090] Example 9. The apparatus of example 1 , comprising a first plurality of RF antennas that include the first RF antenna, and a second plurality of RF antennas that include the second RF antenna, and wherein the at least one processor is further configured to: operate each of the first plurality of RF antennas to transmit respective one or more RF tones; operate each of the second plurality of RF antennas to receive a respective signal while each of the first plurality of RF antennas transmit the respective one or more RF tones, thereby receiving a plurality of signals; and determine a rotational speed of the plurality of rotor blades based on the plurality of signals.

[0091] Example 10. The apparatus of example 9, wherein each RF antenna of the first plurality of RF antennas transmits, when operated by the at least one processor, one or more RF tones at different frequencies than the frequencies of all RF tones transmitted by the other RF antennas of the first plurality of RF antennas.

[0092] Example 11. The apparatus of example 1 , wherein a signal path between the first RF antenna and the second RF antenna passes through a blade envelope of the plurality of rotor blades.

[0093] Example 12. The apparatus of example 1, wherein the at least one processor is further configured to generate a plurality of revolution-matched frequency spectra each corresponding to a respective time period of a plurality of time periods over which the signal was received by the second RF antenna, wherein a duration of each of the plurality of time periods is selected based on the rotational speed of the plurality of rotor blades.

[0094] Example 13. The apparatus of example 12, wherein the at least one processor is further configured to identify an asynchronous vibration based on the plurality of revolution-matched frequency spectra.

[0095] Example 14. The apparatus of example 1, wherein the plurality of RF antennas includes a third RF antenna, wherein the signal received by the second RF antenna is a first signal, and wherein the at least one processor is further configured to: operate the third RF antenna to receive a second signal while the first RF antenna transmits the first RF tone; determine a polarization response of the first signal and second signal as a function of time; and identify rotor whirl of the plurality of rotor blades based on the polarization response.

[0096] Example 15. A method comprising: operating a first radio frequency (RF) antenna arranged within a housing to transmit a first RF tone, wherein the housing comprises a shaft coupled to a plurality of rotor blades; operating a second RF antenna to receive a signal while the first RF antenna transmits the first RF tone; generating, using at least one processor, a frequency spectrum for a portion of the signal received during a first time period; and determining, using the at least one processor, a rotational speed of the plurality of rotor blades during the first time period based on the frequency spectrum.

[0097] Example 16. The method of example 15, wherein the at least one processor is further configured to determine a frequency of at least one vibration of the shaft and / or vibration of one or more of the plurality of rotor blades.

[0098] Example 17. The method of example 15, wherein the at least one processor is configured to operate the first RF antenna to transmit a plurality of RF tones at different frequencies.

[0099] Example 18. The method of example 15, wherein the at least one processor is configured to identify a blade pass frequency based on the frequency spectrum for the portion of the signal, and to determine the rotational speed of the plurality of rotor blades based on blade pass frequency.

[0100] Example 19. The method of example 18, wherein the at least one processor is configured to: identify a plurality of energy peaks in the frequency spectrum for the portion of the signal, the plurality of energy peaks corresponding to harmonics of the blade pass frequency; and identify the blade pass frequency by identifying a frequency of the lowest frequency harmonic of the plurality of energy peaks.

[0101] Example 20. The method of example 15, wherein the at least one processor is configured to generate a plurality of frequency spectra each corresponding to a respective time period of a plurality of time periods over which the signal was received by the second RF antenna, and wherein the rotational speed of the plurality of rotor blades is determined based on the plurality of frequency spectra.

[0102] Such alterations, modifications, and improvements are intended to be part of this disclosure and are intended to be within the spirit and scope of the disclosure. Further, though advantages of the present disclosure are indicated, it should be appreciated that not every embodiment of the technology described herein will include every described advantage. Some embodiments may not implement any features described as advantageous herein and in some instances one or more of the described features may be implemented to achieve further embodiments. Accordingly, the foregoing description and drawings are by way of example only.

[0103] Aspects of the above-described embodiments of the technology described herein can be implemented in any of numerous ways. For example, aspects of the embodiments may be implemented using hardware, software, or a combination thereof.When implemented in software, the software code can be executed on any suitable processor or collection of processors, whether provided in a single computer or distributed among multiple computers. Such processors may be implemented as integrated circuits, with one or more processors in an integrated circuit component, including commercially available integrated circuit components known in the art by names such as CPU chips, GPU chips, microprocessor, microcontroller, or co-processor. Alternatively, a processor may be implemented in custom circuitry, such as an ASIC, or semi-custom circuitry resulting from configuring a programmable logic device. As yet a further alternative, a processor may be a portion of a larger circuit or semiconductor device, whether commercially available, semi-custom or custom. As a specific example, some commercially available microprocessors have multiple cores such that one or a subset of those cores may constitute a processor. Though, a processor may be implemented using circuitry in any suitable format.

[0104] Various aspects of the present disclosure may be used alone, in combination, or in a variety of arrangements not specifically described in the embodiments described in the foregoing and is therefore not limited in its application to the details and arrangement of components set forth in the foregoing description or illustrated in the drawings. For example, aspects described in one embodiment may be combined in any manner with aspects described in other embodiments.

[0105] Also, aspects of the disclosure may be embodied as a method, of which examples have been provided. The acts performed as part of the method may be ordered in any suitable way. Accordingly, embodiments may be constructed in which acts are performed in an order different than illustrated, which may include performing some acts simultaneously, even though shown as sequential acts in illustrative embodiments.

[0106] Use of ordinal terms such as “first,” “second,” “third,” etc., in the claims to modify a claim element does not by itself connote any priority, precedence, or order of one claim element over another or the temporal order in which acts of a method are performed, but are used merely as labels to distinguish one claim element having a certain name from another element having a same name (but for use of the ordinal term) to distinguish the claim elements.

[0107] The terms “approximately” and “about” may be used to mean within ±20% of a target value in some embodiments, within ±10% of a target value in someembodiments, within ±5% of a target value in some embodiments, and yet within ±2% of a target value in some embodiments. The terms “approximately” and “about” may include the target value. The term “substantially equal” may be used to refer to values that are within ±20% of one another in some embodiments, within ±10% of one another in some embodiments, within ±5% of one another in some embodiments, and yet within ±2% of one another in some embodiments.

[0108] The term “substantially” may be used to refer to values that are within ±20% of a comparative measure in some embodiments, within ±10% in some embodiments, within ±5% in some embodiments, and yet within ±2% in some embodiments. For example, a first direction that is “substantially” perpendicular to a second direction may refer to a first direction that is within ±20% of making a 90° angle with the second direction in some embodiments, within ±10% of making a 90° angle with the second direction in some embodiments, within ±5% of making a 90° angle with the second direction in some embodiments, and yet within ±2% of making a 90° angle with the second direction in some embodiments.

[0109] Also, the phraseology and terminology used herein is for the purpose of description and should not be regarded as limiting. The use of “including,” “comprising,” or “having,” “containing,” “involving,” and variations thereof herein, is meant to encompass the items listed thereafter and equivalents thereof as well as additional items.

[0110] What is claimed is:

Claims

CLAIMS1. An apparatus comprising: a housing comprising a shaft coupled to a plurality of rotor blades; a plurality of radio frequency (RF) antennas arranged within the housing, the plurality of RF antennas including a first RF antenna and a second RF antenna; and at least one processor configured to: operate the first RF antenna to transmit a first RF tone; operate the second RF antenna to receive a signal while the first RF antenna transmits the first RF tone; generate a frequency spectrum for a portion of the signal received during a first time period; and determine a rotational speed of the plurality of rotor blades during the first time period based on the frequency spectrum.

2. The apparatus of claim 1, wherein the at least one processor is further configured to determine a frequency of at least one vibration of the shaft and / or vibration of one or more of the plurality of rotor blades.

3. The apparatus of claim 1, wherein the housing comprising a plurality of openings and wherein the first RF antenna and the second RF antenna are each arranged in respective openings in the housing.

4. The apparatus of claim 1, wherein the plurality of RF antennas are dual-polarized RF antennas.

5. The apparatus of claim 1, wherein the at least one processor is configured to operate the first RF antenna to transmit a plurality of RF tones at different frequencies.

6. The apparatus of claim 1, wherein the at least one processor is configured to identify a blade pass frequency based on the frequency spectrum for the portion of thesignal, and to determine the rotational speed of the plurality of rotor blades based on blade pass frequency.

7. The apparatus of claim 6, wherein the at least one processor is configured to: identify a plurality of energy peaks in the frequency spectrum for the portion of the signal, the plurality of energy peaks corresponding to harmonics of the blade pass frequency; and identify the blade pass frequency by identifying a frequency of the lowest frequency harmonic of the plurality of energy peaks.

8. The apparatus of claim 1, wherein the at least one processor is configured to generate a plurality of frequency spectra each corresponding to a respective time period of a plurality of time periods over which the signal was received by the second RF antenna, and wherein the rotational speed of the plurality of rotor blades is determined based on the plurality of frequency spectra.

9. The apparatus of claim 1 , comprising a first plurality of RF antennas that include the first RF antenna, and a second plurality of RF antennas that include the second RF antenna, and wherein the at least one processor is further configured to: operate each of the first plurality of RF antennas to transmit respective one or more RF tones; operate each of the second plurality of RF antennas to receive a respective signal while each of the first plurality of RF antennas transmit the respective one or more RF tones, thereby receiving a plurality of signals; and determine a rotational speed of the plurality of rotor blades based on the plurality of signals.

10. The apparatus of claim 9, wherein each RF antenna of the first plurality of RF antennas transmits, when operated by the at least one processor, one or more RF tones at different frequencies than the frequencies of all RF tones transmitted by the other RF antennas of the first plurality of RF antennas.

11. The apparatus of claim 1 , wherein a signal path between the first RF antenna and the second RF antenna passes through a blade envelope of the plurality of rotor blades.

12. The apparatus of claim 1, wherein the at least one processor is further configured to generate a plurality of revolution-matched frequency spectra each corresponding to a respective time period of a plurality of time periods over which the signal was received by the second RF antenna, wherein a duration of each of the plurality of time periods is selected based on the rotational speed of the plurality of rotor blades.

13. The apparatus of claim 12, wherein the at least one processor is further configured to identify an asynchronous vibration based on the plurality of revolution- matched frequency spectra.

14. The apparatus of claim 1, wherein the plurality of RF antennas includes a third RF antenna, wherein the signal received by the second RF antenna is a first signal, and wherein the at least one processor is further configured to: operate the third RF antenna to receive a second signal while the first RF antenna transmits the first RF tone; determine a polarization response of the first signal and second signal as a function of time; and identify rotor whirl of the plurality of rotor blades based on the polarization response.

15. A method comprising: operating a first radio frequency (RF) antenna arranged within a housing to transmit a first RF tone, wherein the housing comprises a shaft coupled to a plurality of rotor blades; operating a second RF antenna to receive a signal while the first RF antenna transmits the first RF tone; generating, using at least one processor, a frequency spectrum for a portion of the signal received during a first time period; and determining, using the at least one processor, a rotational speed of the plurality of rotor blades during the first time period based on the frequency spectrum.

16. The method of claim 15, wherein the at least one processor is further configured to determine a frequency of at least one vibration of the shaft and / or vibration of one or more of the plurality of rotor blades.

17. The method of claim 15, wherein the at least one processor is configured to operate the first RF antenna to transmit a plurality of RF tones at different frequencies.

18. The method of claim 15, wherein the at least one processor is configured to identify a blade pass frequency based on the frequency spectrum for the portion of the signal, and to determine the rotational speed of the plurality of rotor blades based on blade pass frequency.

19. The method of claim 18, wherein the at least one processor is configured to: identify a plurality of energy peaks in the frequency spectrum for the portion of the signal, the plurality of energy peaks corresponding to harmonics of the blade pass frequency; and identify the blade pass frequency by identifying a frequency of the lowest frequency harmonic of the plurality of energy peaks.

20. The method of claim 15, wherein the at least one processor is configured to generate a plurality of frequency spectra each corresponding to a respective time period of a plurality of time periods over which the signal was received by the second RF antenna, and wherein the rotational speed of the plurality of rotor blades is determined based on the plurality of frequency spectra.

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