A method for rubbing-related fault diagnosis based on MVDR spectrum reconstructed from subspace covariance matrix.

Abstract

This invention discloses a method for tactile feedback fault diagnosis based on MVDR spectrum reconstruction using subspace covariance matrix, belonging to the field of structural vibration state monitoring technology. The method includes blade tip timing data acquisition, blade tip timing signal mathematical model construction, subspace covariance matrix reconstruction, and minimum distortion-free response spectrum estimation. The proposed MVDR spectrum estimation algorithm based on subspace covariance reconstruction is applied to the early identification of tactile feedback faults in rotating blades. This algorithm effectively improves the problems of spurious peak interference, spectral peak distortion, and resolution degradation that easily occur in traditional MVDR under limited snapshot conditions by utilizing subspace orthogonality to reconstruct the covariance matrix. It achieves high-resolution frequency estimation of undersampled BTT signals, providing effective support for early warning of rotating blade faults.

Description

Technical Field

[0001] This invention relates to the field of structural vibration state monitoring technology, and more particularly to a collision and rubbing fault diagnosis method based on MVDR spectrum reconstructed from subspace covariance matrix. More specifically, it relates to a collision and rubbing fault diagnosis method for rotating blades based on a minimum distortion-free response algorithm using blade tip timing raw data and subspace covariance matrix reconstruction. Background Technology

[0002] As a core component of rotating machinery such as aero-engines and turbines, the operating status of the impeller directly affects the safety and stability of the equipment. Under extreme operating conditions, the impeller is subjected to multiple dynamic loads, including centrifugal loads, aerodynamic excitation, and mechanical vibrations, which can easily induce blade resonance, leading to significant stress concentration and accelerated high-cycle fatigue damage. Therefore, real-time monitoring and fault early warning of the operating status of rotating impellers have significant engineering application value.

[0003] As one of the major fault types, friction-impact faults necessitate the development of algorithms specifically designed for them. Current methods for diagnosing friction-impact faults mainly fall into two categories: one based on vibration signal analysis, and the other based on blade tip clearance measurement.

[0004] In vibration signal analysis, changes in vibration characteristics caused by rubbing are often obtained through waveforms, spectra, and shaft center trajectories, including the rotor's natural frequency, displacement and deformation, and the temperature and clearance of the rotor and stator. In blade tip clearance measurement, based on the principle of blade tip clearance measurement, the least squares method is typically used to fit the relationship between the clearance value and the voltage value. Existing research analyzes blade tip clearance at high speeds through eddy current static calibration; improved methods have successfully measured the blade tip clearance of the entire stage of blades; and there are also rubbing monitoring methods based on blade tip clearance sensors, which involve installing blade tip clearance sensors on the casing to collect the distance information between the blade tip and the casing in real time, extracting the radial vibration component of the blade from the clearance signal, and performing time-domain operations to successfully obtain rotor unbalanced vibration information.

[0005] While the aforementioned methods have achieved some success in diagnosing rubbing faults, most research still relies on traditional vibration signal analysis or blade tip clearance measurement. Although Blade Tip Timing (BTT) technology shows significant potential for online monitoring of rotating blades due to its non-contact measurement characteristics, research on rubbing fault diagnosis based on BTT data remains extremely limited due to the undersampling and non-uniform sampling characteristics of BTT signals. Existing signal processing methods are prone to getting trapped in local optima or failing to effectively extract rubbing features when processing this type of data, resulting in a lack of mature and reliable BTT rubbing diagnostic methods. Therefore, there is an urgent need to develop rubbing feature extraction and diagnostic techniques specifically for undersampled BTT signals to fill this research gap. Summary of the Invention

[0006] This invention addresses the shortcomings of existing technologies by providing a method for diagnosing collision and rubbing faults based on MVDR spectra reconstructed from subspace covariance matrices.

[0007] The technical solution of the present invention to solve the above-mentioned technical problems is as follows: A collision fault diagnosis method based on MVDR spectrum reconstructed from subspace covariance matrix includes the following steps: The arrival time data of the rotating blades are collected by the blade tip timing sensor, and the vibration displacement of the blade tip is calculated based on the blade tip timing test principle. The vibration displacement at the blade tip is modeled as a superposition of multiple complex exponential signal components and Gaussian white noise. Multiple snapshot vectors are constructed using an overlapping sliding method to form a signal matrix. The covariance matrix is ​​calculated based on the signal matrix, and eigenvalue decomposition is performed on the covariance matrix to obtain eigenvalues ​​and corresponding eigenvectors. The eigenvectors are divided into signal subspace and noise subspace according to the magnitude of the eigenvalues. The average noise power is obtained by averaging the eigenvalues ​​of the noise subspace. The pure power of each signal component is estimated by the mapping relationship between the matrix trace and the eigenvalues. The covariance matrix after subspace denoising is reconstructed using the estimated pure power and average noise power. Based on the minimum distortion-free response criterion, the minimum distortion-free response pseudo-spectrum is calculated using the reconstructed covariance matrix and steering vector to obtain the frequency estimate of the blade vibration signal; The presence of a rubbing fault can be determined based on the spectral characteristics in the pseudo-spectrum of the minimum distortion response.

[0008] Furthermore, the formula for calculating the vibration displacement d at the blade tip is: ; In the formula, This refers to the actual arrival time of the rotating blade tip; This represents the theoretical arrival time of the rotating blade tip; The shaft frequency of the rotating blade; The radius of the rotating bladed disk; It is pi (π).

[0009] Furthermore, if the vibration displacement at the blade tip is modeled as a superposition of multiple complex exponential signal components and Gaussian white noise, then the mathematical model of the vibration displacement at the blade tip can be expressed as: ; In the above formula, , , Let these represent the amplitude, frequency, and initial phase of the k-th vibration signal, respectively. This represents Gaussian white noise, and it is independent of the vibration signal components. It is a compound exponent.

[0010] Furthermore, multiple snapshot vectors are constructed using an overlapping sliding method, with adjacent snapshots moving backward. J 1 sample, of which J The number of timing sensors at the leaf tip, and the length of each snapshot is... M And satisfy Adjacent snapshots have There are _n_ overlapping samples; where mod represents the remainder after dividing two integers.

[0011] Furthermore, the average noise power is obtained by averaging the eigenvalues ​​of the noise subspace. The calculation formula is as follows: ; In the formula, M represents the average noise power; M represents the snapshot length; K represents the number of signal frequency components. These are the characteristic values ​​arranged in descending order.

[0012] The clean power of each signal component is estimated to obtain the clean signal power. Its formula is: ; In the formula, This represents the pure power of the i-th signal component.

[0013] Furthermore, the subspace-denoised covariance matrix is ​​reconstructed using the estimated pure power and noise power, and its expression is: ; In the formula, This represents the covariance matrix after subspace denoising; These are the corresponding feature vectors; This represents the transpose of the corresponding eigenvector.

[0014] Furthermore, the minimum distortion-free response pseudospectrum is calculated using the reconstructed covariance matrix and steering vector. Its expression is: ; In the formula, Denotes the steering vector, which satisfies ; This represents the transpose of the guide vector.

[0015] Furthermore, the presence of a rubbing fault is determined based on the spectral characteristics of the minimum distortion response pseudo-spectrum. The criterion for determining a rubbing fault is the presence of [missing information - likely a typo or incomplete sentence] in the pseudo-spectrum. n The spectral characteristics of the X / 2 series, where X is the rotating shaft frequency and n is a positive integer.

[0016] Furthermore, the blade tip timing sensor is installed circumferentially along the casing, and there are four sensors. The installation angles of each sensor relative to the reference sensor are 0°, 35°, 45° and 54°, respectively.

[0017] In summary, compared with the prior art, the beneficial effects of the above technical solution are: This invention proposes a method for rubbing fault diagnosis based on MVDR spectrum reconstruction using subspace covariance matrix, and applies it to the early identification of rubbing faults in rotating blades. This method effectively improves the problems of spurious peak interference, spectral peak distortion, and resolution degradation that easily occur in traditional MVDR under limited snapshot conditions by utilizing subspace orthogonality to reconstruct the covariance matrix. It achieves high-resolution frequency estimation of undersampled BTT signals, providing effective support for early warning of rotating blade faults. Attached Figure Description

[0018] Figure 1 This is a flowchart of the method; Figure 2 It consists of BTT data collected by four sensors; Figure 3 It is an MVDR pseudospectral based on subspace reconstruction of the covariance matrix; Figure 4 It is a pseudo-spectral heatmap. Detailed Implementation

[0019] The principles and features of the present invention are described below with reference to all the accompanying drawings. The examples given are only for explaining the present invention and are not intended to limit the scope of the present invention.

[0020] This invention discloses a method for diagnosing collision faults based on MVDR spectra reconstructed from subspace covariance matrices.

[0021] Reference Figures 1-4 A collision fault diagnosis method based on MVDR spectrum reconstructed from subspace covariance matrix includes the following steps: The arrival time data of the rotating blades are collected by the blade tip timing sensor, and the vibration displacement of the blade tip is calculated based on the blade tip timing test principle. The vibration displacement at the blade tip is modeled as a superposition of multiple complex exponential signal components and Gaussian white noise. Multiple snapshot vectors are constructed using an overlapping sliding method to form a signal matrix. The covariance matrix is ​​calculated based on the signal matrix, and eigenvalue decomposition is performed on the covariance matrix to obtain eigenvalues ​​and corresponding eigenvectors. The eigenvectors are divided into signal subspace and noise subspace according to the magnitude of the eigenvalues. The average noise power is obtained by averaging the eigenvalues ​​of the noise subspace. The pure power of each signal component is estimated by the mapping relationship between the matrix trace and the eigenvalues. The covariance matrix after subspace denoising is reconstructed using the estimated pure power and average noise power. Based on the minimum distortion-free response criterion, the minimum distortion-free response pseudo-spectrum is calculated using the reconstructed covariance matrix and steering vector to obtain the frequency estimate of the blade vibration signal; The presence of a rubbing fault can be determined based on the spectral characteristics in the pseudo-spectrum of the minimum distortion response.

[0022] This invention proposes a method for rubbing fault diagnosis based on MVDR spectrum reconstruction using subspace covariance matrix, and applies it to the early identification of rubbing faults in rotating blades. This method effectively improves the problems of spurious peak interference, spectral peak distortion, and resolution degradation that easily occur in traditional MVDR under limited snapshot conditions by utilizing subspace orthogonality to reconstruct the covariance matrix. It achieves high-resolution frequency estimation of undersampled BTT signals, providing effective support for early warning of rotating blade faults.

[0023] The above content will be explained in detail below: Step 1: Collect arrival time data of the rotating blades using a blade tip timing sensor, and calculate the vibration displacement of the blade tip based on the blade tip timing test principle.

[0024] Blade Tip Timing (BTT) is a non-contact method for measuring the vibration of rotating blades. Its core idea is to accurately record the actual arrival time of each blade as it passes the sensor by installing multiple sensors circumferentially on the casing. This time is then compared with the theoretical arrival time under no-vibration conditions. Using the time difference and known parameters such as rotor speed and radius, the vibration displacement of the blade tip can be calculated.

[0025] In this embodiment, the arrival time of the blades is accurately recorded by a blade tip timing sensor on the casing. Based on the BTT test principle, the vibration displacement at the tip of the rotating blade is calculated using the following formula:

[0026] in, This refers to the actual arrival time of the rotating blade tip; This represents the theoretical arrival time of the rotating blade tip; The shaft frequency of the rotating blade; The radius of the rotating bladed disk; It is pi; dThis represents the vibration displacement at the tip of the rotating blade.

[0027] It should be noted that the theoretical arrival time refers to the periodic and predictable time it takes for the blade tip to pass a sensor at a fixed angle when the blade is in an ideal, vibration-free rotational state. This time is determined by the rotor speed, the sensor installation angle, and the circumferential position of the blade.

[0028] The actual arrival time refers to the time it takes for the blade tip to pass the sensor earlier or later if vibration (bending, twisting, or oscillation) occurs during blade rotation. Sensors (such as lasers, fiber optics, or eddy current probes) generate pulse signals when the blade passes by, and the moment of this pulse is recorded as the actual arrival time.

[0029] In a specific embodiment, four tip timing sensors, TIP1, TIP2, TIP3, and TIP4, are installed along the circumferential direction of the blade tip. Sensor TIP1 is used as the reference tip sensor. The relative installation angles of each tip sensor with respect to sensor TIP1 are 0°, 35°, 45°, and 54°, respectively. The rotational frequency of the rotating shaft is acquired using the key phase method. To excite asynchronous resonance of the blade, additional rubbing is applied to excite the blade under gas excitation. The operating frequency of the bladed disk is set to 28.33Hz. Based on the tip timing test principle, the BTT data of blade #7 collected by the four sensors are obtained, as follows: Figure 2 As shown.

[0030] Step 2: Model the vibration displacement of the blade tip as a superposition of multiple complex exponential signal components and Gaussian white noise, and construct multiple snapshot vectors using an overlapping sliding method to form a signal matrix.

[0031] Mathematical model assuming vibration displacement at the blade tip It consists of K frequency components, and each component is a complex exponential signal. Therefore, the mathematical model of the vibration displacement at the blade tip can be expressed as:

[0032] In the above formula, , , Let these represent the amplitude, frequency, and initial phase of the k-th vibration signal, respectively. This represents Gaussian white noise, and it is independent of the vibration signal components. It is a compound exponent.

[0033] L vibration displacements are continuously collected using a blade tip timing sensor. The signal vector of the qth sample is defined as:

[0034] Wherein, the snapshot length M makes J represents the number of BTT sensors. The signal vector referred to as the q-th snapshot; Indicates the first q Vibration displacement corresponding to each sampling; Indicates the first q+ Vibration displacement corresponding to one sampling; Indicates the first q+M- Vibration displacement corresponding to one sampling.

[0035] Adjacent snapshots are constructed using an overlapping sliding mechanism, meaning that each subsequent snapshot moves J samples relative to the previous snapshot, rather than moving one sample at a time. Moving J samples specifically means moving the same number of samples as the number of sensors.

[0036] Continuous snapshots have The overlap of samples M, where M satisfies the following formula:

[0037] Here, mod represents the remainder after dividing two integers.

[0038] The number of snapshots is calculated as follows:

[0039] Where Q represents the number of snapshots; L represents the number of data points.

[0040] Substituting formula (2) into formula (3), we can obtain the expression after the first equal sign in formula (6), which is the signal vector. The complex sinusoidal signal can be expanded as follows:

[0041] in, , Indicates the first i A time difference, Indicates the first q+i The time corresponding to each sampling. Indicates the first q The time corresponding to each sampling.

[0042] Considering the influence of test noise, the blade vibration signal can be written in matrix form. That is, after substituting formula (2) into formula (3) and further simplifying, the matrix form expression of the blade vibration signal is obtained as follows:

[0043]

[0044] Where A represents the array manifold matrix; Indicates the guide vector; Represents a signal vector; Represents the noise vector; and , , They are defined as follows:

[0045] In this embodiment, a mathematical model of the vibration displacement at the blade tip is assumed. It consists of K=3 frequency components, and each frequency component is a complex exponential signal. The mathematical model of the vibration displacement at the blade tip is modeled as shown in formula (2). 512 data points are continuously collected by the blade tip timing sensor. The signal vector of the qth sampling is defined as shown in formula (3). In formula (3), the snapshot length M=32, making... J=4, where J is the number of sensors.

[0046] The adjacent snapshots are constructed using an overlapping sliding method, meaning that the next snapshot moves 4 samples backward relative to the previous snapshot, instead of moving 1 sample at a time. Therefore, the number of snapshots Q = 121.

[0047] The blade vibration signal is written in matrix form, that is, the signal matrix expression is shown in equation (7).

[0048] Step 3: Calculate the covariance matrix based on the signal matrix, and perform eigenvalue decomposition on the covariance matrix to obtain eigenvalues ​​and corresponding eigenvectors. Divide the eigenvectors into signal subspace and noise subspace according to the magnitude of the eigenvalues. Average the eigenvalues ​​of the noise subspace to obtain the noise power, and estimate the pure power of each signal component through the mapping relationship between the matrix trace and the eigenvalues. Reconstruct the subspace-denoised covariance matrix using the estimated pure power and noise power.

[0049] Assuming signal vector With noise vector The samples are uncorrelated, thus the sample covariance matrix can be calculated. for:

[0050] in, Represents the expectation operator; Represents the conjugate transpose of a signal vector; This represents the transpose of the array manifold matrix; Indicates the noise variance; denoted as the identity matrix; P indicates that the covariance matrix of the blade vibration signal vector itself is a positive definite matrix.

[0051]

[0052] Introducing subspace theory to the sample covariance matrix Eigenvalue decomposition yields the following equation:

[0053] in, The eigenvalues ​​are arranged in descending order; These are the corresponding eigenvectors. The first K largest eigenvalues ​​correspond to the signal subspace. The remaining MK smaller eigenvalues ​​correspond to the noise subspace. ; Indicates the transpose of the signal subspace; This indicates the transpose of the noise subspace; N and S have no real meaning and are only used to distinguish between signal and noise.

[0054] In this embodiment, the first three larger eigenvalues ​​correspond to the signal subspace. That is, K=3, and there are MK remaining, which is 32-3=29 corresponding noise subspaces. .

[0055] Assumption It has zero mean and variance. For white noise, according to eigenvalue decomposition theory, the smaller MK eigenvalues ​​correspond to the noise power. To improve estimation accuracy, the noise power is averaged to obtain the average noise power. The calculation formula is as follows:

[0056] Simultaneously, based on the mapping relationship between the properties of the matrix trace and its eigenvalues, the pure power of the i-th signal component is estimated, thus obtaining the pure signal power. Estimate using the following formula:

[0057] The mapping relationship between the properties of the matrix trace and its eigenvalues ​​is expressed by the following formula: ; In the formula, Represent the covariance matrix; This represents the trace of the covariance matrix.

[0058] Utilizing the separated pure signal power With mean noise variance The covariance matrix after subspace denoising is reconstructed. As shown in formula (15). In this process, the original fluctuating noise subspace is replaced by the variance of uniformly distributed white noise, while the energy of all real signal components is preserved for subsequent peak estimation.

[0059]

[0060] Step 4: Based on the minimum distortion-free response criterion, calculate the minimum distortion-free response pseudo-spectrum using the reconstructed covariance matrix and steering vector to obtain the frequency estimate of the blade vibration signal.

[0061] The core idea of ​​MVDR (Minimum Distortion Response) is to design an optimal filter that allows the target frequency component to pass through without distortion, while suppressing other frequency components and noise to the greatest extent. The minimum variance of the final output is the power estimate for that frequency.

[0062] Let the filter weight vector be... The output signal of the filter Recorded as:

[0063] in, This represents the transpose of the weight vector.

[0064] Output signal The power can be expressed as:

[0065] The filter coefficients should be set under distortion-free constraints, meaning the filter's response at the tentative frequency f should be normalized to 1.

[0066] in, To meet The theoretical frequency steering vector. This constraint guarantees that the input signal passes through the filter weight vector. At that time, along the direction vector The signal will not be distorted. Meanwhile, signals along other vector directions tend to be attenuated. This leads to the following minimization problem:

[0067] The cost function is constructed and solved using the Lagrange multiplier method. The solution formula is as follows:

[0068] In the above formula, Represents the Lagrange multipliers; Thus, the optimal filter coefficients at the true frequency f are obtained. The calculation formula is as follows:

[0069] The MVDR spectrum of the input signal is defined by the output power of its optimal filter. Solving equation (22) yields... Substituting directly into formula (18), we can obtain a concise expression for the MVDR pseudospectrum based on the subspace-reconstructed covariance matrix, as follows:

[0070] in, This represents the minimal distortion-free response pseudospectrum.

[0071] The reconstructed covariance matrix after subspace denoising Substituting into equation (22), we can obtain Figure 3 , Figure 4 The pseudo-spectral diagram and response thermogram shown can be used to analyze the spectral characteristics of the nX / 2 series corresponding to the rubbing fault that occurs under this working condition.

[0072] Step 5: Determine whether there is a rubbing fault based on the spectral characteristics in the pseudo-spectrum of the minimum distortion response.

[0073] The criterion for judging the rubbing fault is: the appearance of [something] in the pseudo-spectrum. n The spectral characteristics of the X / 2 series, where X is the rotating shaft frequency and n is a positive integer.

[0074] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for diagnosing collision-related faults based on MVDR spectra reconstructed from subspace covariance matrices, characterized in that, Includes the following steps: The arrival time data of the rotating blades are collected by the blade tip timing sensor, and the vibration displacement of the blade tip is calculated based on the blade tip timing test principle. The vibration displacement at the blade tip is modeled as a superposition of multiple complex exponential signal components and Gaussian white noise. Multiple snapshot vectors are constructed using an overlapping sliding method to form a signal matrix. The covariance matrix is ​​calculated based on the signal matrix, and eigenvalue decomposition is performed on the covariance matrix to obtain eigenvalues ​​and corresponding eigenvectors. The eigenvectors are divided into signal subspace and noise subspace according to the magnitude of the eigenvalues. The average noise power is obtained by averaging the eigenvalues ​​of the noise subspace. The pure power of each signal component is estimated by the mapping relationship between the matrix trace and the eigenvalues. The covariance matrix after subspace denoising is reconstructed using the estimated pure power and the average noise power, which is the reconstructed covariance matrix. Based on the minimum distortion-free response criterion, the minimum distortion-free response pseudo-spectrum is calculated using the reconstructed covariance matrix and steering vector to obtain the frequency estimate of the blade vibration signal; The presence of a rubbing fault can be determined based on the spectral characteristics in the pseudo-spectrum of the minimum distortion response.

2. The collision fault diagnosis method based on MVDR spectrum reconstructed from subspace covariance matrix according to claim 1, characterized in that, The formula for calculating the vibration displacement d at the blade tip is: ； In the formula, This refers to the actual arrival time of the rotating blade tip; This represents the theoretical arrival time of the rotating blade tip; The shaft frequency of the rotating blade; The radius of the rotating bladed disk; It is pi (π).

3. The collision fault diagnosis method based on MVDR spectrum reconstructed from subspace covariance matrix according to claim 2, characterized in that, If the vibration displacement at the blade tip is modeled as a superposition of multiple complex exponential signal components and Gaussian white noise, then the mathematical model of the vibration displacement at the blade tip is... Represented as: ； In the above formula, , , Let these represent the amplitude, frequency, and initial phase of the k-th vibration signal, respectively. This represents Gaussian white noise, which is independent of the vibration signal components. It is a compound exponent.

4. The collision fault diagnosis method based on MVDR spectrum reconstructed from subspace covariance matrix according to claim 1, characterized in that, Multiple snapshot vectors are constructed using an overlapping sliding method. Adjacent snapshots are shifted backward by J samples, where J is the number of leaf tip timing sensors. The length of each snapshot is M, and the following conditions are met: Adjacent snapshots have There are _n_ overlapping samples; where mod represents the remainder after dividing two integers.

5. The collision fault diagnosis method based on MVDR spectrum reconstructed from subspace covariance matrix according to claim 1, characterized in that, The average noise power is obtained by averaging the eigenvalues ​​of the noise subspace. The formula for its calculation is: ； In the formula, M represents the average noise power; M represents the snapshot length; K represents the number of signal frequency components. These are the characteristic values ​​arranged in descending order.

6. The collision fault diagnosis method based on MVDR spectrum reconstructed from subspace covariance matrix according to claim 5, characterized in that, The clean power of each signal component is estimated to obtain the clean signal power. The calculation formula is as follows: ； In the formula, This represents the pure power of the i-th signal component.

7. The collision fault diagnosis method based on MVDR spectrum reconstructed from subspace covariance matrix according to claim 6, characterized in that, The subspace-denoised covariance matrix is ​​reconstructed using the estimated pure power and average noise power, and its expression is: ； In the formula, This represents the covariance matrix after subspace denoising; These are the corresponding feature vectors; This represents the transpose of the corresponding eigenvector.

8. The collision fault diagnosis method based on MVDR spectrum reconstructed from subspace covariance matrix according to claim 7, characterized in that, Calculate the minimum distortion-free response pseudospectrum using the reconstructed covariance matrix and steering vector. Its expression is: ； In the formula, Describes the steering vector, which satisfies ; This represents the transpose of the guide vector.

9. The collision fault diagnosis method based on MVDR spectrum reconstructed from subspace covariance matrix according to claim 1, characterized in that, The presence of a rubbing fault is determined based on the spectral characteristics in the pseudo-spectrum of the minimum distortion response. The criteria for determining a rubbing fault are: the appearance of [symbols / features] in the pseudo-spectrum. n The spectral characteristics of the X / 2 series, where X is the rotating shaft frequency and n is a positive integer.

10. The collision fault diagnosis method based on MVDR spectrum reconstructed from subspace covariance matrix according to claim 1, characterized in that, The blade tip timing sensor is installed circumferentially along the casing. There are four sensors, and the installation angles of each sensor relative to the reference sensor are 0°, 35°, 45° and 54°, respectively.

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