Bayesian inference method and system for solving frequency aliasing

Abstract

The invention discloses a Bayesian inference method and system for solving frequency aliasing, and the method comprises the steps: arranging a sensor 1 and a sensor 2 on a receiver to form a non-uniform layout; obtaining an aliasing frequency sequence f = {f1, f2,..., fM} according to measurement data X = {x1, x2,..., xN} from a sensor 1 and weak prior information, wherein the weak prior information is the possible range of the inherent frequency of the blade; and substituting the aliasing frequency sequence f and measurement data Y = {y1, y2,..., yN} from the sensor 2 into a Bayesian inference formula, calculating and normalizing the support degree p (fiY) of each aliasing frequency, and taking the frequency fi with the highest support degree as the real inherent frequency fn.

Description

Bayesian inference method and system for frequency aliasing removal Technical Field

[0001] This invention relates to the field of rotating machinery blade vibration technology, and in particular to a Bayesian inference method and system for de-aliasing frequency. Background Technology

[0002] As a key component of rotating machinery, the health status of rotor blades, under high-speed rotation and complex loads, directly affects the operational safety and performance of the equipment. Blade tip timing measurement technology, as a non-contact online monitoring method, has unique advantages in practical scenarios where structural constraints and the number of sensors are limited.

[0003] However, due to the constraints of sensor layout and the sparsity of measurement points, the acquired leaf tip timing signals usually suffer from severe undersampling, resulting in significant aliasing of the signal spectrum. The true frequency information is masked or distorted, and how to recover the correct natural frequency from the aliased signal becomes a difficult problem.

[0004] Existing sensor-limited methods for extracting the natural frequency of blade tip timing signals largely rely on strong prior information, i.e., a narrow range of predicted blade natural frequencies. However, this prior information is unavailable when the blade is damaged and fails when the rotational speed changes rapidly. Therefore, how to achieve frequency identification of severely undersampled blade tip timing signals under weak prior conditions and reduce reliance on prior information has become a core problem that urgently needs to be solved in blade structural health monitoring.

[0005] The information disclosed in the background section is only for enhancing the understanding of the background of this invention, and therefore may contain information that does not constitute prior art known to those skilled in the art. Summary of the Invention

[0006] This invention provides a Bayesian inference method and system for frequency aliasing removal. It uses two sensors to meet the requirements of actual installation location and fewer sensors. It utilizes Bayesian inference and combines weak prior information to overcome the undersampling problem, and accurately extracts the inherent frequency information of the blade from the aliasing spectrum of the blade tip timing signal.

[0007] A Bayesian inference method for de-aliasing includes:

[0008] Step 1: Arrange sensor 1 and sensor 2 on the casing to form a non-uniform layout;

[0009] Step 2: Based on the measurement data X={x1,x2,…,x...} from sensor 1 N The aliasing frequency sequence f = {f1, f2, ..., f} is obtained from weak prior information. M The weak prior information is the possible range of the blade's natural frequencies;

[0010] Step 3: Combine the aliasing frequency sequence f with the measurement data Y={y1,y2,…,y...} from sensor 2. N Substituting into the Bayesian inference formula, calculate and normalize the support p(f) for each aliasing frequency. i |Y), take the frequency f with the highest support. i As the true inherent frequency f n .

[0011] In the Bayesian inference method for frequency aliasing, sensor 1 is installed at an angle of α1, sensor 2 is installed at an angle of α2, and |α2-α1|≠180°.

[0012] In the Bayesian inference method for de-aliasing, the weak prior information is fprior=[fp1,fp2], where fp1 and fp2 represent the upper and lower bounds of the prior information, respectively, fp1 is less than fp2, and fp2-fp1 is greater than twice the rotational speed frequency.

[0013] In the Bayesian inference method for frequency aliasing, step 3 includes:

[0014] Step 3.1: Noise It follows a mean of 0 and a variance of . The signal parameters are a normal distribution, with amplitude A of the natural frequency component, amplitude B of the transition frequency component, and phase of the natural frequency component. All obey no prior information. Where p(A) represents the probability distribution of the amplitude A of the natural frequency component, and p(B) represents the probability distribution of the amplitude B of the transition frequency component. () represents the phase of the natural frequency component. The probability distribution,

[0015] Step 3.2: Based on the aliasing frequency sequence f, the sensor 1 measurement data X, and the measurement time sequence t x Estimating signal parameters It includes the amplitude of the natural frequency component A, the amplitude of the transition frequency component B, and the phase of the natural frequency component. Estimate the frequency corresponding to f i signal parameters for:

[0016]

[0017] Solving this system of equations yields the result corresponding to the frequency f. i signal parameters ;

[0018] Step 3.3: Utilize the estimated signal parameters The amplitude of the natural frequency component A, the amplitude of the transition frequency component B, and the phase of the natural frequency component. Estimating noise variance of distribution

[0019] Wherein, the corresponding frequency f i variance The estimation formula is as follows:

[0020]

[0021] Step 3.4: Based on the measurement data Y from sensor 2 and the estimated signal parameters ,variance Substitute the values ​​into the Bayesian inference formula, calculate the support for each aliasing frequency, and normalize it. The frequency with the highest support after normalization is selected as the true intrinsic frequency f. n .

[0022] In the Bayesian inference method for de-aliasing, the Bayesian inference formula is as follows:

[0023]

[0024] in , For the support of the unnormalized frequency fi,

[0025] The normalization formula is:

[0026] .

[0027] In the Bayesian inference method for resolving frequency aliasing, the least squares method is used to solve the system of equations.

[0028] In the Bayesian inference method for de-aliasing, frequency shift reconstruction or virtual sampling technology is used to alias the frequency sequence f, which includes: mapping the original undersampled signal to multiple possible frequency bands based on rotational speed information and sensor layout, forming a frequency set covering all possible aliased copies within the weak prior information.

[0029] In the Bayesian inference method for de-aliasing, the angular interval between sensor 1 and sensor 2 is less than 30°.

[0030] A system for implementing the Bayesian inference method for frequency aliasing includes:

[0031] Sensor 1 and Sensor 2 are arranged in a non-uniform layout on the casing;

[0032] The data acquisition module is used to synchronously acquire two leaf-end timing signals;

[0033] The signal processing unit is configured to execute a Bayesian inference method to output an estimated value of the blade's natural frequency.

[0034] The early warning module triggers an early warning based on an estimated intrinsic frequency.

[0035] Compared with the prior art, the present invention has the following advantages: the present invention solves the problems of undersampling of blade tip timing measurement signals and reliance on strong prior information, and can quickly and accurately extract the natural frequency of rotating blades from the aliased spectrum. Attached Figure Description

[0036] Various other advantages and benefits of the present invention will become apparent to those skilled in the art upon reading the detailed description of the preferred embodiments below. The accompanying drawings are for illustrative purposes only and are not intended to limit the invention. It is obvious that the drawings described below are merely some embodiments of the invention, and those skilled in the art can obtain other drawings based on these drawings without any inventive effort. Furthermore, the same reference numerals denote the same parts throughout the drawings.

[0037] In the attached diagram:

[0038] Figure 1 is a flowchart of a Bayesian inference method for de-aliasing provided in an embodiment of this disclosure;

[0039] Figure 2 is a schematic diagram of a non-uniform sensor layout for a Bayesian inference method for frequency aliasing resolution provided in an embodiment of this disclosure.

[0040] Figure 3 is a frequency identification comparison diagram of a Bayesian inference method for de-aliasing provided in an embodiment of this disclosure.

[0041] The present invention will be further explained below with reference to the accompanying drawings and embodiments. Detailed Implementation

[0042] Specific embodiments of the invention will now be described in more detail with reference to the accompanying drawings. While specific embodiments of the invention are shown in the drawings, it should be understood that the invention may be implemented in various forms and should not be limited to the embodiments set forth herein. Rather, these embodiments are provided so that this invention will be thorough and complete, and will fully convey the scope of the invention to those skilled in the art.

[0043] It should be noted that certain terms are used in the specification and claims to refer to specific components. Those skilled in the art will understand that different terms may be used to refer to the same component. This specification and claims do not distinguish components based on differences in terminology, but rather on differences in function. The terms "comprising" or "including" used throughout the specification and claims are open-ended and should be interpreted as "comprising but not limited to." The following descriptions are preferred embodiments for carrying out the invention; however, these descriptions are for the purpose of understanding the general principles of the specification and are not intended to limit the scope of the invention. The scope of protection of this invention is determined by the appended claims.

[0044] To facilitate understanding of the embodiments of the present invention, further explanations and descriptions will be provided below with reference to the accompanying drawings and specific embodiments. The accompanying drawings do not constitute a limitation on the embodiments of the present invention.

[0045] As shown in Figures 1 to 3, the Bayesian inference method for de-aliasing includes the following steps:

[0046] Step 1: Arrange sensor 1 and sensor 2 on the casing to form a non-uniform layout;

[0047] It should be noted that the casing refers to the shell structure that houses the blades, which are essentially stationary.

[0048] Step 2: Based on the measurement data X={x1,x2,…,x...} from sensor 1 N The aliasing frequency sequence f = {f1, f2, ..., f} is obtained from weak prior information. M The weak prior information is the possible range of the blade's natural frequencies;

[0049] Step 2.1: Select any virtual frequency f m Determine the amplitude of the natural frequency component A 1m and phase φ 1m Frequency component amplitude A rm and phase φ rm According to the following formula and the time series t={t1, t2, ..., t3} of the measurement data X from sensor 1, N Generate a set of virtual signals Y m ;

[0050]

[0051] Among them, f rm This represents the frequency of the frequency conversion component, which is determined based on the time series t in the measurement data X from sensor 1.

[0052] Step 2.2: Based on the virtual signal Ym Construct another set of virtual signals Y n The expression is as follows:

[0053]

[0054] Where A 1n =A 1m ,f 1n =f 1m , φ 1m =φ 1n .

[0055] Step 2.3: Convert the virtual signal Y m and Y n The product signal S is obtained by multiplying the data X measured by sensor 1 by the product signal X. xym and S xyn dot product of signal S xym and S xyn Performing discrete Fourier transforms on each spectrum P yields the corresponding spectrum P. xym and P xyn ;

[0056] Step 2.4: Spectrum P xym With P xyn The difference is used to obtain the spectrum P. mn Extracting spectrum P mn The highest frequency component f in a ;

[0057] Step 2.5: Based on the highest frequency component f a Combined with sensor 1 measurement data X, and weak prior information (denoted as f) prior =[f p1 , f p2 ], where f p1 and f p2 These represent prior information, namely the upper and lower bounds of the blade's natural frequency range, f. p1 Less than f p2 Calculate the aliasing frequency sequence f={f1,f2,…,f M}

[0058] Calculate the aliasing frequency sequence f using the following formula:

[0059] ,

[0060] Where K is a coefficient, taking values ​​within the range of positive integers, such that the frequency of f is... prior Inside, f rm It is the frequency of the frequency conversion component;

[0061] Step 3: Combine the aliasing frequency sequence f with the measurement data Y={y1,y2,…,y...} from sensor 2. N Substituting into the Bayesian inference formula, calculate and normalize the support p(f) for each aliasing frequency. i |Y), take the frequency f with the highest support. i As the true inherent frequency f n .

[0062] In a preferred embodiment of the Bayesian inference method for frequency aliasing, the sensor 1 is installed at an angle of α1, the sensor 2 is installed at an angle of α2, and |α2-α1|≠180°.

[0063] In a preferred embodiment of the Bayesian inference method for frequency aliasing, the weak prior information is fprior=[fp1, fp2], where fp1 and fp2 represent the upper and lower bounds of the prior information, respectively, fp1 is less than fp2, and fp2-fp1 is greater than twice the rotational speed frequency.

[0064] In a preferred embodiment of the Bayesian inference method for frequency aliasing, step 3 includes:

[0065] Step 3.1: Noise It follows a mean of 0 and a variance of . The signal parameters are a normal distribution, with amplitude A of the natural frequency component, amplitude B of the transition frequency component, and phase of the natural frequency component. All obey no prior information. Where p(A) represents the probability distribution of the amplitude A of the natural frequency component, and p(B) represents the probability distribution of the amplitude B of the transition frequency component. () represents the phase of the natural frequency component. The probability distribution,

[0066] Step 3.2: Based on the aliasing frequency sequence f i Sensor 1 measurement data X and measurement time series t x Estimating signal parameters It includes frequencies corresponding to f i The amplitude of the natural frequency component A i Frequency component amplitude B i Phase of natural frequency components Estimate the frequency corresponding to f i signal parameters for:

[0067]

[0068] Solving this system of equations yields the result corresponding to the frequency f. isignal parameters ;

[0069] Step 3.3: Utilize the estimated signal parameters The amplitude of the natural frequency component A, the amplitude of the transition frequency component B, and the phase of the natural frequency component. Estimating noise variance of distribution

[0070] Wherein, the corresponding frequency f i variance The estimation formula is as follows:

[0071]

[0072] Step 3.4: Based on the measurement data Y from sensor 2 and the estimated signal parameters ,variance Substitute the values ​​into the Bayesian inference formula, calculate the support for each aliasing frequency, and normalize it. The frequency with the highest support after normalization is selected as the true intrinsic frequency f. n。

[0073] In a preferred embodiment of the Bayesian inference method for frequency aliasing, the Bayesian inference formula is:

[0074]

[0075] in , For the support of the unnormalized frequency fi,

[0076] The normalization formula is:

[0077] .

[0078] In a preferred embodiment of the Bayesian inference method for resolving frequency aliasing, the least squares method is used to solve the system of equations.

[0079] In a preferred embodiment of the Bayesian inference method for de-aliasing, the frequency sequence f is aliased using frequency shift reconstruction or virtual sampling technology, which includes: mapping the original undersampled signal to multiple possible frequency bands based on rotational speed information and sensor layout, forming a frequency set covering all possible aliased copies within the weak prior information.

[0080] In a preferred embodiment of the Bayesian inference method for frequency aliasing, the angular interval between sensor 1 and sensor 2 is less than 30°.

[0081] A system for implementing the Bayesian inference method for frequency aliasing includes:

[0082] Sensor 1 and Sensor 2 are arranged in a non-uniform layout on the casing;

[0083] The data acquisition module is used to synchronously acquire two leaf-end timing signals;

[0084] The signal processing unit is configured to execute a Bayesian inference method to output an estimated value of the blade's natural frequency.

[0085] The early warning module triggers an early warning based on an estimated intrinsic frequency.

[0086] In one embodiment, a Bayesian inference method for de-aliasing includes the following steps:

[0087] Step 1: Arrange sensor 1 and sensor 2 on the casing to form a non-uniform layout, as shown in Figure 2;

[0088] Step 2: Based on the measurement data X={x1,x2,…,x...} from sensor 1 N The aliasing frequency sequence f = {f1, f2, ..., f} is obtained from weak prior information. M};

[0089] Step 3: Combine the aliasing frequency sequence f with the sensor 2 measurement data Y={y1,y2,…,y N Substituting into the Bayesian inference formula, calculate and normalize the support p(f) for each aliasing frequency. i |Y), take the frequency f with the highest support. i As the true inherent frequency f n .

[0090] In the Bayesian inference method for frequency aliasing, in step 1, the non-uniform layout formed by sensor 1 and sensor 2 refers to the fact that the interval between sensor 1 and sensor 2 is not 180°. The installation angle of sensor 1 is recorded as α1 and the installation angle of sensor 2 is recorded as α2. Then, |α2-α1|≠180°.

[0091] Preferably, the distance between the two sensors should be as small as possible.

[0092] In the Bayesian inference method for frequency aliasing, in step 2, weak prior information refers to the possible range of intrinsic frequencies, denoted as f. prior =[f p1 , f p2 ], where f p1 and f p2 f represents the upper and lower bounds of prior information (i.e., the natural frequency range of the blade), respectively. p1 Less than fp2 Where f p2 -f p1 It can be much greater than twice the rotational speed frequency.

[0093] In the Bayesian inference method for frequency aliasing, step 3 includes:

[0094] Step 3.1: Assume noise It follows a mean of 0 and a variance of . The signal parameters are a normal distribution, with amplitude A of the natural frequency component, amplitude B of the transition frequency component, and phase of the natural frequency component. All obey no-information priors, that is Where p(A) represents the probability distribution of the amplitude A of the natural frequency component, and p(B) represents the probability distribution of the amplitude B of the transition frequency component. () represents the phase of the natural frequency component. The probability distribution.

[0095] Step 3.2: Based on the aliasing frequency sequence f, the sensor 1 measurement data X, and the measurement time sequence t x Estimating signal parameters This includes the amplitude of the natural frequency component A, the amplitude of the transition frequency component B, and the phase of the natural frequency component. .

[0096] Step 3.2 estimates the frequency f. i signal parameters The method is as follows:

[0097]

[0098] Solving this system of equations yields the result corresponding to the frequency f. i signal parameters ,

[0099] Preferably, the least squares method can be used to solve the system of equations.

[0100] Step 3.3: Using the estimated signal parameters, the amplitude of the natural frequency component A, the amplitude of the transition frequency component B, and the phase of the natural frequency component... Estimating noise variance of distribution ,

[0101] Wherein, the corresponding frequency f i variance The estimation formula is as follows:

[0102]

[0103] Step 3.4: Based on the measurement data Y from sensor 2 and the estimated signal parameters ,variance Substitute the values ​​into the Bayesian inference formula, calculate the support for each aliasing frequency, and normalize it. The frequency with the highest support after normalization is selected as the true intrinsic frequency f. n

[0104] The Bayesian inference formula used in step 3.4 is:

[0105]

[0106] in , The support for the unnormalized frequency fi.

[0107] The normalization formula is:

[0108]

[0109] In one embodiment, a Bayesian inference method for de-aliasing includes the following steps:

[0110] Step 1: Sensor 1 is installed at position α1=0°, and sensor 2 is installed at position α2=9.7297°, with an interval of 9.7297°.

[0111] Step 2: Given weak prior information f prior =[0, 1500] Hz, using sensor 1 to measure data X={x1,x2,…,x N Based on the weak prior information, the aliasing frequency sequence f={67,93,147,173,227,253,307,333,387,413,467,493,547,573,627,563,707,733,787,813,867,893,947,973,1027,1053,1107,1133,1187,1213,1267,1293,1347,1373,1427,1453}Hz was extracted.

[0112] Step 3.1: Assume noise It follows a mean of 0 and a variance of . The signal parameters are a normal distribution, with amplitude A of the natural frequency component, amplitude B of the transition frequency component, and phase of the natural frequency component. All obey no-information priors, that is Where p(A) represents the probability distribution of the amplitude A of the natural frequency component, and p(B) represents the probability distribution of the amplitude B of the transition frequency component. () represents the phase of the natural frequency component. The probability distribution.

[0113] Step 3.2: Using the aliasing frequency sequence f, sensor 1 measurement data X, and measurement time series t x Estimating signal parameters The formula is as follows:

[0114]

[0115] The signal parameters are obtained by using the least squares method. .

[0116] Step 3.3: Using the estimated signal parameters, the amplitude of the natural frequency component A, the amplitude of the transition frequency component B, and the phase of the natural frequency component... Estimating noise variance of distribution ,

[0117] Wherein, the corresponding frequency f i variance The estimation formula is as follows:

[0118]

[0119] Step 3.4: Based on the measurement data Y from sensor 2 and the estimated signal parameters ,variance Substitute the values ​​into the Bayesian inference formula, calculate the support for each aliasing frequency, and normalize it. The frequency with the highest support after normalization is selected as the true intrinsic frequency f. n

[0120] The Bayesian inference formula used in step 3.4 is:

[0121]

[0122] in , The unnormalized frequency f i Support level.

[0123] The normalization formula is:

[0124]

[0125] The normalized frequency-support results are shown in Figure 3. The frequency 413Hz was selected as the true natural frequency f. n。

[0126] The above methods can be used to recover the true natural frequency components of aliasing. By analyzing the changes in natural frequencies, the working status of the blade can be determined, thereby realizing blade status monitoring.

[0127] This disclosure uses only one blade tip timing sensor, which overcomes the limitations of actual installation location and layout while achieving the minimum number of sensors used. It constructs different virtual signals using the frequency shift principle, extracts characteristic frequencies by frequency shifting, solves the frequency aliasing problem caused by undersampling, and extracts the blade's inherent frequency.

[0128] Furthermore, the non-uniform dual-sensor layout of this invention (e.g., a 9.73° interval instead of 180°) breaks the periodic spectral extension caused by traditional symmetrical arrangements, resulting in distinguishable phase and amplitude differences in the aliasing behavior of the same real frequency at the two sensors. This small but crucial geometric asymmetry provides a physical basis for subsequently using data from the second sensor to identify the aliasing candidate set generated by the first sensor.

[0129] Secondly, this invention relies only on broad, weak prior information (e.g., natural frequencies in the 0–1500 Hz range), and combines rotational speed and sampling timing to automatically generate a candidate frequency set covering all possible aliased replicas through a frequency shift mapping mechanism. This process does not require prior knowledge of the precise modal range, which is significantly better than the dependence of existing methods on "narrow-band strong priors," and is especially suitable for operating conditions where the natural frequencies shift significantly after blade damage such as cracks or chipping.

[0130] Third, for each candidate frequency, a physical signal model incorporating the dominant vibration frequency and rotational frequency components is fitted using the data from the first sensor. The amplitude, phase, and other parameters are then efficiently estimated using the least squares method, and the residual noise variance is calculated accordingly. This modeling process transforms the frequency identification problem into a parameterized signal reconstruction problem, providing a reliable likelihood function basis for Bayesian inference.

[0131] This invention introduces Bayesian inference as a frequency selection criterion: the measured data from the second sensor is treated as an independent validation set, the explanatory power (i.e., likelihood probability) of each candidate frequency model for that data is calculated, and the posterior support is obtained by normalization. This mechanism is essentially a data-driven model selection that can automatically suppress erroneous candidates caused by noise, harmonics, or spurious aliasing. Even if multiple frequencies show similar peak values ​​in the spectrum of the first sensor, the true frequency can be accurately selected through "cross-validation" from the second perspective.

[0132] This method achieves high-confidence deambiguation of severely aliased spectra with a minimal hardware configuration using only two sensors in a non-uniform layout. Experiments show that even under complex operating conditions such as varying rotational speed, prior failure, and low signal-to-noise ratio, this method can still stably identify the true intrinsic frequency (e.g., accurately identifying 413 Hz, as shown in Figure 3), with low computational complexity, allowing it to run in real-time on embedded platforms. Compared to traditional FFT peak interpretation or multi-sensor array methods, this invention achieves an excellent balance between sensor number and layout, prior dependence, anti-aliasing capability, and engineering feasibility, providing a lightweight and highly robust new solution for online health monitoring of rotating machinery blades.

[0133] Although embodiments of the present invention have been described above in conjunction with the accompanying drawings, the present invention is not limited to the specific embodiments and application fields described above. The specific embodiments described above are merely illustrative and instructive, and not restrictive. Those skilled in the art can make many other forms based on the guidance of this specification and without departing from the scope of protection of the claims of the present invention, and all of these are within the scope of protection of the present invention.

Claims

1. A Bayesian inference method for de-aliasing, characterized in that, The process includes the following steps: Step 1: Arrange sensor 1 and sensor 2 on the housing to form a non-uniform layout; Step 2: Based on the measurement data X={x1,x2,…,x...} from sensor 1... N The aliasing frequency sequence f = {f1, f2, ..., f} is obtained from weak prior information. M }, the weak prior information is the possible range of the blade's natural frequencies; Step 3: Combine the aliasing frequency sequence f with the measurement data Y={y1,y2,…,y from sensor 2. N Substituting into the Bayesian inference formula, calculate and normalize the support p(f) for each aliasing frequency. i |Y), take the frequency f with the highest support. i As the true inherent frequency f n .

2. The Bayesian inference method for de-aliasing according to claim 1, characterized in that, Preferably, the sensor 1 is installed at an angle of α1, the sensor 2 is installed at an angle of α2, and |α2-α1|≠180°.

3. The Bayesian inference method for de-aliasing according to claim 1, characterized in that, The weak prior information is fprior=[fp1, fp2], where fp1 and fp2 represent the upper and lower bounds of the prior information, respectively. fp1 is less than fp2, and fp2-fp1 is greater than twice the rotational speed frequency.

4. The Bayesian inference method for de-aliasing according to claim 1, characterized in that, Step 3 includes: Step 3.1: Noise It follows a mean of 0 and a variance of . The signal parameters are a normal distribution, with the amplitude A of the natural frequency component, the amplitude B of the transition frequency component, and the phase of the natural frequency component. All obey no prior information. Where p(A) represents the probability distribution of the amplitude A of the natural frequency component, and p(B) represents the probability distribution of the amplitude B of the transition frequency component. () represents the phase of the natural frequency component. The probability distribution, step 3.2: Based on the aliasing frequency sequence f, the sensor 1 measurement data X and the measurement time sequence t x Estimating signal parameters It includes the amplitude of the natural frequency component A, the amplitude of the transition frequency component B, and the phase of the natural frequency component. Estimate the frequency corresponding to f i signal parameters for: Where {t1,t2,…,tN} is the sampling time sequence corresponding to the measurement data {x1,x2,…,xN} of sensor 1; Bi is the amplitude of the frequency component in the blade vibration signal, which corresponds to the frequency f. i Ai represents the amplitude of the natural frequency component in the blade vibration signal, corresponding to the frequency f. i ; It is the phase of the inherent component in the blade vibration signal, which corresponds to the frequency f. i Solving this system of equations yields the result corresponding to the frequency f. i signal parameters Step 3.3: Utilize the estimated signal parameters The amplitude of the natural frequency component A, the amplitude of the transition frequency component B, and the phase of the natural frequency component. Estimating noise variance of distribution Wherein, the corresponding frequency f i variance The estimation formula is as follows: Step 3.4: Based on the measurement data Y from sensor 2 and the estimated signal parameters ,variance Substitute the values ​​into the Bayesian inference formula, calculate the support for each aliasing frequency, and normalize it. The frequency with the highest support after normalization is selected as the true intrinsic frequency f. n .

5. A Bayesian inference method for de-aliasing according to claim 4, characterized in that, The Bayesian inference formula is as follows: ;in Y is the measurement data from sensor 2. The support for the unnormalized frequency fi is given by the normalization formula: 。 6. A Bayesian inference method for de-aliasing according to claim 4, characterized in that, The system of equations is solved using the least squares method.

7. A Bayesian inference method for de-aliasing according to claim 1, characterized in that, The frequency sequence f is aliased using frequency shift reconstruction or virtual sampling techniques, which includes: mapping the original undersampled signal to multiple possible frequency bands based on rotational speed information and sensor layout, forming a frequency set that covers all possible aliased copies within the weak prior information.

8. A Bayesian inference method for de-aliasing according to claim 1, characterized in that, The angular interval between sensor 1 and sensor 2 is less than 30°.

9. A system for implementing a Bayesian inference method for frequency aliasing according to any one of claims 1-8, characterized in that, It includes: Sensor 1 and Sensor 2 are arranged in a non-uniform layout on the casing; The data acquisition module is used to synchronously acquire two leaf-end timing signals; The signal processing unit is configured to execute a Bayesian inference method to output an estimated value of the blade's natural frequency; the early warning module triggers an early warning based on the estimated value of the natural frequency.

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