Leaf tip timing time-frequency non-convex compressed sensing method and system based on multiple measurement vectors

Abstract

The invention discloses a leaf tip timing signal time-frequency non-convex compressed sensing method and a leaf tip timing signal time-frequency non-convex compressed sensing system. The method comprises the following steps: firstly, mounting a blade end timing sensor at the circumferential position of a rotor blade casing, and acquiring an actual time sequence when a rotor blade reaches the blade end timing sensor; then, a multi-measurement snapshot matrix is constructed according to the time difference formed by the ideal time and the actual time when the rotor blade reaches the blade end timing sensor, and the rotation frequency and the rotation radius of the rotor blade; thirdly, constructing a multi-measurement vector time-frequency non-convex compressed sensing model based on the multi-measurement snapshot matrix; and finally, solving the multi-measurement-vector time-frequency non-convex compressed sensing model under an optimization-minimization framework to obtain a rotor blade vibration signal time-frequency diagram which is used for sensing the crack fault condition of the rotor blade. According to the method, a single-measurement-vector compressed sensing model is expanded to a multi-measurement-vector compressed sensing model, the blade tip timing data reconstruction time is greatly shortened, and stable indexes are expected to be provided for blade crack monitoring and diagnosis.

Description

Technical Field

[0001] The present invention belongs to the technical field of non-contact measurement of rotor blades of rotating machinery, and in particular relates to a method and system for time-frequency non-convex compression sensing of blade tip timing signals. Background Art

[0002] Rotating blades may experience vibration problems when operating under complex working conditions, which not only reduces their fatigue life and performance, but may also lead to serious accidents. As a non-contact measurement technology, blade tip timing technology can measure the arrival time of blades during operation to obtain vibration data. However, the sampling characteristics of blade tip timing signals usually do not conform to Shannon sampling theorem, and the sparse characteristics of the signals in the time-frequency domain have not been fully utilized.

[0003] In the prior art, Fourier transform-based analysis methods face challenges in processing blade tip timing signals because these signals are usually non-uniformly undersampled. Although sparse reconstruction methods can be used to reconstruct undersampled signals, existing compressed sensing models have limitations in parameter identification accuracy and anti-interference ability. Summary of the invention

[0004] In order to overcome the above problems, the present invention proposes a method and system for non-convex time-frequency compression sensing of blade tip timing signals. First, a blade tip timing sensor is installed at a circumferential position of a rotor blade casing, and the actual time series of the rotor blade reaching the blade tip timing sensor is obtained; then, a multi-measurement snapshot matrix is ​​constructed based on the time difference between the ideal time and the actual time when the rotor blade reaches the blade tip timing sensor, the rotor blade rotation frequency and the rotation radius; then, a multi-measurement vector time-frequency non-convex compression sensing model is constructed based on the multi-measurement snapshot matrix; finally, the multi-measurement vector time-frequency non-convex compression sensing model is solved under the optimization-minimization framework to obtain a rotor blade vibration signal time-frequency diagram, which is used to perceive the rotor blade crack fault condition. The method expands the single measurement vector compression sensing model to a multi-measurement vector compression sensing model, breaking through the deficiency of the existing compression sensing model that only uses the frequency domain sparsity of the blade vibration signal; and greatly reduces the reconstruction time of batch blade tip timing data, obtains the vibration signal time-frequency diagram at full speed of the blade, and is expected to provide a robust indicator for blade crack monitoring and diagnosis, thereby completing the present invention.

[0005] Specifically, the purpose of the present invention is to provide the following aspects:

[0006] On the one hand, a time-frequency non-convex compressed sensing method for blade tip timing signals is provided, the method comprising:

[0007] Step 1, installing a blade tip timing sensor at a circumferential position of a rotor blade casing, and obtaining an actual time series of the rotor blade reaching the blade tip timing sensor;

[0008] Step 2, constructing a multi-measurement snapshot matrix according to the time difference between the ideal time and the actual time when the rotor blade reaches the blade tip timing sensor, the rotor blade rotation frequency and the rotation radius;

[0009] Step 3, constructing a multi-measurement vector time-frequency non-convex compressed sensing model based on the multi-measurement snapshot matrix;

[0010] Step 4, solving the multi-measurement vector time-frequency non-convex compressed sensing model under the optimization-minimization framework to obtain the rotor blade vibration signal time-frequency diagram, wherein the rotor blade vibration signal time-frequency diagram is used to sense the rotor blade crack fault condition.

[0011] In step 1, the number of excited modes is first determined and recorded as , determine the number of blade tip timing sensors according to the number of modes ; Afterwards, The blade tip timing sensors are installed at circumferential positions on the rotor blade casing.

[0012] in, .

[0013] The distribution angle and position of the blade tip timing sensor are determined based on the particle swarm optimization algorithm to ensure that the sampling points of the blade tip timing sensor can effectively cover all excitation modes.

[0014] In step 1, the actual time when the rotor blade arrives at the blade tip timing sensor is arranged into a series of data points according to the snapshot time sequence to obtain the actual time series.

[0015] In step 2, the ideal time for the rotor blade to arrive at the blade tip timing sensor is expressed as: ; is the rotor blade serial number, is the blade tip timing sensor number, Indicates the number of circles, Indicates the frequency conversion. Indicates The installation angle of each sensor, Indicates the serial number is The installation angle of the blades.

[0016] The vibration displacement of the rotor blade is obtained by the following formula: ; is the rotor blade speed, is the radius of rotation, The time difference between the ideal time and the actual time when the rotor blade reaches the blade tip timing sensor.

[0017] In step 2, the ideal time for the rotor blade to arrive at the blade tip timing sensor is arranged into a series of data points in snapshot time order to obtain an ideal time series.

[0018] In a second aspect, a time-frequency non-convex compressed sensing system for blade tip timing signals is provided, the system comprising:

[0019] A blade tip timing sensor layout module, which is used to install blade tip timing sensors at circumferential positions of the rotor blade casing and obtain a time series of the rotor blades reaching the blade tip timing sensors;

[0020] A vibration displacement calculation module, which is used to construct a multi-measurement snapshot matrix based on the time difference between the ideal time and the actual time when the rotor blade reaches the blade tip timing sensor, the rotor blade rotation frequency and the rotation radius;

[0021] The rotor blade vibration parameter identification module is used to construct a multi-measurement vector time-frequency non-convex compressed sensing model based on a multi-measurement snapshot matrix.

[0022] The system also includes: a fault diagnosis module, which is used to solve a multi-measurement vector time-frequency non-convex compressed sensing model under an optimization-minimization framework to obtain a rotor blade vibration signal time-frequency diagram, and the rotor blade vibration signal time-frequency diagram is used to sense the rotor blade crack fault condition.

[0023] The beneficial effects of the present invention include:

[0024] (1) The blade tip timing signal time-frequency non-convex compressed sensing method provided by the present invention uses a multi-measurement snapshot matrix composed of the vibration displacement of the rotor blades and establishes a multi-measurement vector time-frequency non-convex compressed sensing model, which is solved under the MM framework, making it possible to recover a complete vibration signal from the severely undersampled blade tip vibration displacement signal.

[0025] (2) The non-convex time-frequency compressed sensing method of the blade tip timing signal provided by the present invention reconstructs the undersampled BTT signal through a sparse reconstruction method, which helps to comprehensively extract the potential rotor blade vibration information and produce more accurate vibration parameter identification results.

[0026] (3) The non-convex time-frequency compressed sensing method for blade tip timing signals provided by the present invention expands the single measurement vector compressed sensing model to a multi-measurement vector compressed sensing model, which overcomes the deficiency of the existing compressed sensing model that only utilizes the sparse frequency domain of blade vibration signals.

[0027] (4) Compared with the classical compressed sensing model under the SMV framework, the non-convex compressed sensing method for blade tip timing signal time-frequency provided by the present invention makes full use of the row sparseness of the coefficient matrix under continuous sampling, which can reduce the probability of atomic misselection, suppress the interference of the rotational frequency and its multiple frequencies under variable speed conditions, improve the accuracy and robustness of the time-frequency reconstruction of vibration signals within the full operating speed range, and significantly reduce the reconstruction time of batch blade tip timing data, thereby obtaining the vibration time-frequency diagram of the blade at full speed, and is expected to provide a robust indicator for blade crack monitoring and diagnosis.

[0028] (5) The blade tip timing signal time-frequency non-convex compressed sensing system provided by the present invention effectively processes and analyzes the blade tip timing signal through the coordinated work of the blade tip timing sensor layout module, the vibration displacement calculation module, the rotor blade vibration parameter identification module and the rotor blade vibration fault diagnosis module, thereby providing a robust indicator for rotor blade crack monitoring and diagnosis. BRIEF DESCRIPTION OF THE DRAWINGS

[0029] By reading the detailed description of the preferred specific embodiments below, various other advantages and benefits of the present invention will become clear to those of ordinary skill in the art. The drawings in the specification are only used for the purpose of illustrating the preferred embodiments and are not considered to be limitations of the present invention. Obviously, the drawings described below are only some embodiments of the present invention. For those of ordinary skill in the art, other drawings can also be obtained based on these drawings without creative work.

[0030] In the attached picture:

[0031] Figure 1 A flow chart of the time-frequency non-convex compressed sensing method of blade tip timing signal of the present invention is shown;

[0032] Figure 2 A time domain diagram of the vibration response of one of the blades measured in the embodiment is shown;

[0033] FIG3 (a) shows a time-frequency diagram of a rotor blade vibration signal obtained by analyzing a conventional method based on SMV in an embodiment;

[0034] FIG3( b ) shows a time-frequency diagram of the vibration signal of the rotor blades obtained by analyzing the MMV method of the present invention in an embodiment. DETAILED DESCRIPTION

[0035] The following will refer to the attached Figure 13 (b) to describe specific embodiments of the present invention in more detail. Although specific embodiments of the present invention are shown in the accompanying drawings, it should be understood that the present invention can be implemented in various forms and should not be limited by the embodiments described herein. On the contrary, these embodiments are provided to enable a more thorough understanding of the present invention and to fully convey the scope of the present invention to those skilled in the art.

[0036] It should be noted that certain words are used in the specification and claims to refer to specific components. Those skilled in the art should understand that technicians may use different nouns to refer to the same component. This specification and claims do not use the difference in nouns as a way to distinguish components, but use the difference in the functions of the components as the criterion for distinction. As mentioned throughout the specification and claims, "including" or "comprising" is an open term, so it should be interpreted as "including but not limited to". The subsequent description of the specification is a preferred embodiment of the present invention, but the description is based on the general principles of the specification and is not intended to limit the scope of the present invention. The scope of protection of the present invention shall be determined by the attached claims.

[0037] In the description of the present invention, it should be noted that the terms "upper", "lower", "inner", "outer", "front", "rear", etc. indicate positions or positional relationships based on the working state of the present invention, and are only for the convenience of describing the present invention and simplifying the description, rather than indicating or implying that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation, and therefore cannot be understood as limiting the present invention. In addition, the terms "first", "second", "third", and "fourth" are only used for descriptive purposes and cannot be understood as indicating or implying relative importance.

[0038] To facilitate understanding of the embodiments of the present invention, further explanation will be given below by taking specific embodiments as examples in conjunction with the accompanying drawings, and each of the accompanying drawings does not constitute a limitation on the embodiments of the present invention.

[0039] On the one hand, according to a time-frequency non-convex compressed sensing method of a blade tip timing signal provided by the present invention, the method comprises:

[0040] Step 1, installing a blade tip timing sensor at a circumferential position of a rotor blade casing, and obtaining an actual time series of the rotor blade reaching the blade tip timing sensor;

[0041] Step 2, constructing a multi-measurement snapshot matrix according to the time difference between the ideal time and the actual time when the rotor blade reaches the blade tip timing sensor, the rotor blade rotation frequency and the rotation radius;

[0042] Step 3, constructing a multi-measurement vector time-frequency non-convex compressed sensing model based on the multi-measurement snapshot matrix;

[0043] Step 4, solving the multi-measurement vector time-frequency non-convex compressed sensing model under the optimization-minimization framework to obtain the rotor blade vibration signal time-frequency diagram, wherein the rotor blade vibration signal time-frequency diagram is used to sense the rotor blade crack fault condition.

[0044] The time-frequency non-convex compressed sensing method of the blade tip timing signal is described in detail below.

[0045] Step 1: Install a blade tip timing sensor at a circumferential position of a rotor blade casing, and obtain an actual time series of the rotor blade reaching the blade tip timing sensor.

[0046] In step 1, the number of excited modes is first determined and recorded as , determine the number of blade tip timing sensors according to the number of modes ,in ; Afterwards, The blade tip timing sensors are installed in the circumferential position of the rotor blade casing; then, the distribution angle and position of the blade tip timing sensors are determined based on the particle swarm optimization algorithm to ensure that the sampling points of the blade tip timing sensors can effectively cover all the excited modes, thereby improving the accuracy and reliability of modal parameter identification.

[0047] Further, Usually 4~10.

[0048] In step 1, the collected pulse signal is preprocessed to obtain the actual time when the rotor blade reaches the blade tip timing sensor. , its physical meaning is The rotor blades are The actual arrival time of the circle The actual time of each blade tip timing sensor.

[0049] In step 1, the actual time when the rotor blade reaches the blade tip timing sensor is arranged into a series of data points according to the snapshot time sequence, so as to obtain the actual time series.

[0050] Furthermore, the preprocessing includes: collecting blade tip timing data, selecting a predetermined threshold for the original pulse signal, and screening the first The rotor blades are The actual arrival time of the circle The actual time of the blade tip timing sensor The threshold is generally chosen to be half of the pulse peak value.

[0051] Step 2: construct a multi-measurement snapshot matrix based on the time difference between the ideal time and the actual time when the rotor blade reaches the blade tip timing sensor, the rotor blade rotation frequency and the rotation radius.

[0052] In step 2, the ideal time for the rotor blade to arrive at the blade tip timing sensor is expressed as: ,in, is the rotor blade serial number, is the blade tip timing sensor number, Indicates the number of circles, Indicates the shaft rotation frequency. Indicates The installation angle of the blade tip timing sensor, Indicates the serial number is The ideal time series is understood as the ideal time for the rotor blade to reach the blade tip timing sensor arranged as a series of data points in snapshot time order.

[0053] Furthermore, the time difference between the theoretical arrival time of the rotor blade tip under the ideal condition without blade vibration and the actual arrival time measured in step 1 is obtained by the following formula: Arrange them into a series of data points in the order of snapshot time to get the sequence time difference.

[0054] In step 2, the time difference between the theoretical arrival time and the actual arrival time of the rotor blade tip is calculated. , rotor blade speed and the radius of rotation Obtain the vibration displacement of the rotor blade tip: Arranging them into a series of data points in the order of snapshot time can obtain a single measurement snapshot vector, i.e., the sequence number The rotor blades are in serial number of Tip timing sensor rotation The vibration displacement data vector obtained from each cycle.

[0055] Furthermore, the single-measurement snapshot vector is transformed into a multi-measurement snapshot matrix, which is specifically expressed as:

[0056] D = [ d ( 1 ) ， d ( 2 ) ， … ， d ( l ) ] = [ d i , 1 1 d i , 1 n + 1 ⋯ d i , 1 ( l − 1 ) n + 1 ⋮ ⋮ ⋱ ⋮ d i , N p 1 d i , N p n + 1 ⋯ d i , N p ( l − 1 ) n + 1 ⋮ ⋮ ⋱ ⋮ d i , 1 n d i , 1 2 n ⋯ d i , 1 l n ⋮ ⋮ ⋱ ⋮ d i , N p n d i , N p 2 n ⋯ d i , N p l n ] ,in Indicates A single measurement snapshot vector.

[0057] Furthermore, the multi-measurement snapshot matrix is ​​understood as the snapshots of all rotor blades within a certain period of time. The matrix composed of the vibration displacement data vectors measured by the blade tip timing sensors reflects the vibration state of the rotor blades in multiple rotation cycles.

[0058] Step 3: construct a multi-measurement vector time-frequency non-convex compressed sensing model based on the multi-measurement snapshot matrix.

[0059] In the prior art, the compressed sensing method based on single measurement vector (SMV) utilizes the sparsity of the blade tip timing signal in the frequency domain, but fails to utilize its sparse prior in the time and frequency domain, resulting in limited parameter identification accuracy and the ability to resist rotation frequency and frequency multiplication interference. The inventors found that for a multi-measurement snapshot matrix composed of multiple consecutive snapshot vectors, the vectors have the same spectral structure but different amplitudes. This type of problem belongs to the category of multiple measurement vectors (MMV). MMV can be regarded as solving multiple SMVs at the same time when the sparse transformation matrix remains unchanged. Based on this, multiple single measurement snapshot matrices (i.e., the vibration displacement of multiple-turn blade tip timing sensors) are combined into a multi-measurement snapshot matrix, which makes up for the deficiency of the existing model that only utilizes the sparsity of the frequency domain. MMV makes full use of the row sparse characteristics of the coefficient matrix, reduces the probability of atomic misselection, suppresses the rotation frequency and its frequency multiplication interference under variable speed conditions, improves the aggregation and robustness of the time-frequency reconstruction of the blade vibration signal within the full working speed range, and significantly reduces the signal reconstruction time when processing batch blade tip timing sensor data.

[0060] According to a preferred embodiment, step 3 comprises the following steps:

[0061] Step 3-1, converting the vibration displacement of the rotor blade into superimposed vibration displacements of each order of modal vibrations;

[0062] Step 3-2, obtaining a sparse representation equation of the rotor blade vibration according to the superimposed vibration displacements of each order of the modal vibrations;

[0063] Step 3-3, obtaining a sparse transformation matrix according to the sparse representation equation of the rotor blade vibration;

[0064] Step 3-4, based on the sparse transformation matrix, a multi-measurement vector time-frequency non-convex compressed sensing model is obtained.

[0065] In step 3-1, the vibration displacement of the rotor blade is converted into superimposed vibration displacements of each order mode, which is expressed as: , For rotor blade The modal vibration frequency, and Respectively is the coefficient of the blade vibration equation of the order, and m is the number of excited modes.

[0066] In step 3-2, the superimposed vibration displacements of each order are combined with the first Modal vibration frequency With The excitation order corresponding to the first mode The relationship between: , the vibration displacement expression is further expressed as: . Combine it with the relation: , and further obtain the sparse representation equation of the rotor blade vibration: , M is the number of modes of interest.

[0067] In step 3-3, according to the sparse representation equation of the rotor blade vibration, the sparse transformation matrix is ​​obtained:

[0068] F = [ s i n ( D E O i 1 ) c o s ( D E O i 1 ) ⋯ s i n ( N D E O i 1 ) c o s ( N D E O i 1 ) ⋮ ⋮ ⋱ ⋮ ⋮ s i n ( D E O i N p ) c o s ( D E O i N p ) ⋯ s i n ( N D E O i N p ) s i n ( N D E O i N p ) ⋮ ⋮ ⋱ ⋮ ⋮ s i n ( D E O ( i 1 + 2 ∗ ( n − 1 ) π ) c o s ( D E O ( i 1 + 2 ∗ ( n − 1 ) π ) ⋯ s i n ( N D E O ( i 1 + 2 ∗ ( n − 1 ) π ) c o s ( N D E O ( i 1 + 2 ∗ ( n − 1 ) π ) ⋮ ⋮ ⋱ ⋮ ⋮ s i n ( D E O ( i N p + 2 ∗ ( n − 1 ) π ) c o s ( D E O ( i N p + 2 ∗ ( n − 1 ) π ) ⋯ s i n ( N D E O ( i N p + 2 ∗ ( n − 1 ) π ) c o s ( N D E O ( i N p + 2 ∗ ( n − 1 ) π ) ] ,in is the excitation order resolution of the reconstructed signal, is the number of frequency components of the reconstructed signal, then the identified frequency range is [ D E O , 2 D E O , ⋯ , N D E O ] , the maximum frequency component of the reconstructed signal is: .

[0069] In step 3-4, the coefficients of the sparse representation equation of the rotor blade vibration corresponding to each frequency component form a sparse representation coefficient matrix:

[0070] S = [ a 1 1 1 a 1 1 2 ⋯ a 1 1 l a 2 1 1 a 2 1 2 ⋯ a 2 1 l ⋮ ⋮ ⋱ ⋮ a 1 N 1 a 1 N 2 ⋯ a 1 N l a 2 N 1 a 2 N 2 ⋯ a 2 N l ] , then the multi-measurement snapshot matrix , sparse transformation matrix and the sparse representation coefficient matrix The relationship is: , which is the sparse representation equation for reconstructing undersampled signals.

[0071] Furthermore, through This equation is solved to reconstruct the undersampled BTT signal. But for the sparse representation coefficient matrix The solution of is an underdetermined problem, and the uniqueness of the solution is difficult to guarantee. The convex optimization sparse reconstruction method of the norm has the problem of underestimation, and the amplitude reconstruction accuracy is low, while the classical orthogonal matching pursuit algorithm has low robustness and limited frequency identification accuracy under low signal-to-noise ratio conditions. In order to solve the problem of reduced reconstruction accuracy caused by the underestimation of signal feature amplitude by the classical compressed sensing model, the present invention further establishes a multi-measurement vector time-frequency non-convex compressed sensing model based on the sparse representation equation of the reconstructed undersampled signal, which is expressed as:

[0072] a r g m i n S α ‖ S l ‖ 2 , p + β ‖ S [ : ] ‖ p ( 0 < p < 1 ) s . t . D = F S ,

[0073] in, Represents the sparse representation coefficient matrix No. row vector, Indicates a broad norm, and is a generalized norm with row-sparse structure, which can promote row sparsity. Promote sparsity between elements, α and β are weighting coefficients. The multi-measurement vector time-frequency non-convex compressed sensing model has the characteristics of inducing a structure that satisfies row sparsity and a general sparse structure, and has a non-convex optimization model with stronger prior information.

[0074] To facilitate further solution, the multi-measurement vector time-frequency non-convex compressed sensing model is expressed as an equivalent unconstrained optimization model:

[0075] m i n i m i z e S { f ( S ) = 1 2 ‖ D − F S ‖ F 2 + l 1 ( ∑ l = 1 L ‖ S l ‖ 2 p ) + l 2 ‖ S [ : ] ‖ p p }

[0076] in, is the regularization parameter, is the number of rows of the sparse representation coefficient matrix. Encodes the row-sparse prior, l 2 ‖ S [ : ] ‖ p p The model promotes sparsity between elements and mathematically encodes the time-frequency sparse prior of the vibration signal. However, the coupling between variables makes it difficult to solve.

[0077] Step 4: Solve the multi-measurement vector time-frequency non-convex compressed sensing model under the optimization-minimization framework to obtain the time-frequency diagram of the rotor blade vibration signal.

[0078] The inventors have found that solving the above-mentioned multi-measurement vector time-frequency non-convex compressed sensing model under the optimization-minimization (MM) framework can achieve indirect solution of the objective function, which can ensure the efficiency and robustness of the solution process. By comparing with the multi-measurement signal data at the same time, the atoms with the most relevant frequencies in the sparse transformation dictionary are selected to reduce the probability of incorrect atomic selection, suppress the rapidly changing frequency components and their multiples, and retain the effective information in the spectrum to the maximum extent, and draw the time-frequency diagram of the rotor blade vibration signal to perform rotor blade crack fault diagnosis.

[0079] Furthermore, the MM algorithm is used to optimize the objective function by optimizing the proxy function.

[0080] According to a preferred embodiment, step 4 comprises the following steps:

[0081] Step 4-1, using an optimization-minimization algorithm to construct a proxy function of the objective function of the multi-measurement vector time-frequency non-convex compressed sensing model;

[0082] Step 4-2, indirectly solving the proxy function of the objective function to obtain a sparse representation coefficient matrix;

[0083] Step 4-3, solving the sparse representation coefficient matrix to obtain the vibration parameters of the rotor blades;

[0084] Step 4-4, obtaining a time-frequency diagram of the rotor blade vibration signal according to the rotor blade vibration parameters.

[0085] In step 4-1, the optimization-minimization algorithm is used to optimize the objective function by optimizing the proxy function. The key lies in the construction of the proxy function. The constructed proxy function is:

[0086] ,in, is the proxy function of the objective function in each iterative solution process, For the The result of the iteration is called for 's proxy function.

[0087] Furthermore, in order to ensure the stability and convergence of the solution, the objective function is constructed based on the second-order Taylor expansion idea. Finally, the proxy function of the objective function is obtained:

[0088]

[0089] in, For variables Irrelevant constants, is a weight matrix with row sparsity structure, and is a weighted matrix with sparse structure between elements. The proxy function achieves complete decoupling between variables. Then, in each iteration, the closed-form solution is:

[0090]

[0091] In step 4-3, the sparse representation coefficient matrix is ​​solved to obtain Estimates. Includes the kth vibration equation coefficient , , thus obtaining the k-order vibration equation: , where the amplitude , is the vibration angular frequency, and the number of vibration frequency components is the number of vibration modes.

[0092] In the present invention, high-speed rotor blades often work under extremely severe vibration, centrifugal force and temperature conditions. High-cycle fatigue generated under low stress and high-frequency vibration is a common cause of blade damage, and severe vibration will cause blade cracks. When a blade has cracks, the blade's natural frequency will drop significantly. The vibration frequency and amplitude of the rotor blade are analyzed through the time-frequency diagram of the rotor blade vibration signal, and the dynamic frequency offset is found, thereby discovering the rotor blade crack fault condition.

[0093] In the present invention, the undersampled BTT signal is reconstructed by a sparse reconstruction method, which helps to fully extract the potential blade vibration information and produce more accurate vibration parameter identification results. The method fully exploits the time-frequency sparse characteristics of the rotor blade signal, constructs a multi-measurement snapshot matrix composed of blade tip vibration displacement, and establishes a multi-measurement vector time-frequency non-convex compressed sensing model, breaking through the limitation of only using frequency domain sparsity. The multi-measurement vector time-frequency non-convex compressed sensing model is solved using the MM framework, making it possible to recover the complete vibration signal from the severely undersampled blade tip vibration displacement signal. Compared with the classic compressed sensing model under the SMV framework, the non-convex compressed sensing model under the MMV framework makes full use of the row sparsity characteristics of the coefficient matrix under continuous sampling, which can reduce the probability of atomic misselection, suppress the rotational frequency and its multiple frequency interference under variable speed conditions, improve the accuracy and robustness of the time-frequency reconstruction of the vibration signal within the full working speed range, and greatly reduce the reconstruction time of batch blade tip timing data, so as to obtain the vibration signal time-frequency diagram at full speed of the blade, and is expected to provide a robust indicator for blade crack monitoring and diagnosis.

[0094] On the other hand, a blade tip timing signal time-frequency non-convex compressed sensing system, the system comprising:

[0095] A blade tip timing sensor layout module, which is used to install blade tip timing sensors at circumferential positions of the rotor blade casing and obtain a time series of the rotor blades reaching the blade tip timing sensors;

[0096] A vibration displacement calculation module, which is used to construct a multi-measurement snapshot matrix based on the time difference between the ideal time and the actual time when the rotor blade reaches the blade tip timing sensor, the rotor blade rotation frequency and the rotation radius;

[0097] The rotor blade vibration parameter identification module is used to construct a multi-measurement vector time-frequency non-convex compressed sensing model based on a multi-measurement snapshot matrix.

[0098] A fault diagnosis module is used to solve a multi-measurement vector time-frequency non-convex compressed sensing model under an optimization-minimization framework to obtain a rotor blade vibration signal time-frequency diagram, wherein the rotor blade vibration signal time-frequency diagram is used to sense a rotor blade crack fault condition.

[0099] The present invention is further described below by means of specific examples.

[0100] In one embodiment, the number of excited modes is determined , blade tip timing sensor =8, based on the particle swarm optimization algorithm, the optimal layout angle of each blade tip timing sensor is determined as:

[0101] , shaft speed Keep it at about 116.7Hz, select half of the pulse peak value of the collected pulse signal as the threshold, and get the actual time after screening.

[0102] The time difference between the theoretical arrival time and the actual arrival time of the rotor blade tip , rotor blade speed and the radius of rotation Obtain the vibration displacement of the rotor blade tip: , and then construct a single measurement snapshot vector, which is composed of The circle vibration displacement data vector is composed of 10 snapshots in total, and a multi-measurement snapshot matrix constructed by 10 single-measurement snapshot vectors is obtained, that is, a matrix with 160 rows and 10 columns is obtained. Figure 2 The time domain diagram of the measured vibration response of one of the blades is shown.

[0103] The vibration displacement of the rotor blade is converted into superimposed vibration displacements of each order modal. According to the superimposed vibration displacements of each order modal, the sparse representation equation of the vibration of the rotor blade is obtained. According to the sparse representation equation of the vibration of the rotor blade, the sparse transformation matrix is ​​obtained in combination with the installation angles of each sensor, namely:

[0104] F = [ s i n ( D E O i 1 ) c o s ( D E O i 1 ) ⋯ s i n ( N D E O i 1 ) c o s ( N D E O i 1 ) ⋮ ⋮ ⋱ ⋮ ⋮ s i n ( D E O i N p ) c o s ( D E O i N p ) ⋯ s i n ( N D E O i N p ) s i n ( N D E O i N p ) ⋮ ⋮ ⋱ ⋮ ⋮ s i n ( D E O ( i 1 + 2 ∗ ( n − 1 ) π ) c o s ( D E O ( i 1 + 2 ∗ ( n − 1 ) π ) ⋯ s i n ( N D E O ( i 1 + 2 ∗ ( n − 1 ) π ) c o s ( N D E O ( i 1 + 2 ∗ ( n − 1 ) π ) ⋮ ⋮ ⋱ ⋮ ⋮ s i n ( D E O ( i N p + 2 ∗ ( n − 1 ) π ) c o s ( D E O ( i N p + 2 ∗ ( n − 1 ) π ) ⋯ s i n ( N D E O ( i N p + 2 ∗ ( n − 1 ) π ) c o s ( N D E O ( i N p + 2 ∗ ( n − 1 ) π ) ]

[0105] Among them, the excitation order resolution Set to 0.01, the number of frequency components of the reconstructed signal Set it to 1000, and you get a matrix with 180 rows and 2000 columns.

[0106] On the basis of the above, a multi-measurement vector time-frequency non-convex compressed sensing model is established:

[0107] a r g m i n S α ‖ S l ‖ 2 , p + β ‖ S [ : ] ‖ p ( 0 < p < 1 ) s . t . D = F S , which can be expressed as an equivalent unconstrained optimization model:

[0108] m i n i m i z e S { f ( S ) = 1 2 ‖ D − F S ‖ F 2 + l 1 ( ∑ l = 1 L ‖ S l ‖ 2 p ) + l 2 ‖ S [ : ] ‖ p p } .

[0109] The optimization-minimization algorithm is used to construct the proxy function of the model's objective function, and the proxy function of the objective function is indirectly solved to obtain the sparse representation coefficient matrix. , the coefficients of each order vibration equation of the rotor blade are obtained, thereby obtaining the blade vibration parameters. Figure 3 (a) shows the time-frequency diagram of the rotor blade vibration signal obtained by the traditional SMV method. It can be seen that the identified rotor blade frequency is about 653Hz, which is consistent with the results of strain gauge and finite element analysis. Figure 3 (b) shows the time-frequency diagram of the rotor blade vibration signal obtained by the MMV method of the present invention. It can be seen that the noise in the signal is almost filtered out, and the effective information is retained to the maximum extent.

[0110] The present invention is described in detail above in combination with preferred embodiments and exemplary examples. However, it should be noted that these specific embodiments are only illustrative explanations of the present invention and do not constitute any limitation on the protection scope of the present invention. Without exceeding the spirit and protection scope of the present invention, various improvements, equivalent substitutions or modifications may be made to the technical content of the present invention and its embodiments, which all fall within the protection scope of the present invention. The protection scope of the present invention shall be subject to the attached claims.

Claims

1. A time-frequency non-convex compressed sensing method for blade tip timing signals, characterized in that: The method comprises: Step 1, installing a blade tip timing sensor at a circumferential position of a rotor blade casing, and obtaining an actual time series of the rotor blade reaching the blade tip timing sensor; Step 2, constructing a multi-measurement snapshot matrix according to the time difference between the ideal time and the actual time when the rotor blade reaches the blade tip timing sensor, the rotor blade rotation frequency and the rotation radius; Step 3, constructing a multi-measurement vector time-frequency non-convex compressed sensing model based on the multi-measurement snapshot matrix; Step 4, solving the multi-measurement vector time-frequency non-convex compressed sensing model under the optimization-minimization framework to obtain the rotor blade vibration signal time-frequency diagram, wherein the rotor blade vibration signal time-frequency diagram is used to sense the rotor blade crack fault condition.

2. The method according to claim 1, characterized in that Preferably, in step 1, the number of excited modes is first determined and recorded as , determine the number of blade tip timing sensors according to the number of modes ; Afterwards, The blade tip timing sensors are installed at circumferential positions on the rotor blade casing.

3. The method according to claim 2, characterized in that 。 4. The method according to claim 2, characterized in that: The distribution angle and position of the blade tip timing sensor are determined based on the particle swarm optimization algorithm to ensure that the sampling points of the blade tip timing sensor can effectively cover all excitation modes.

5. The method according to claim 1, characterized in that In step 1, the actual time when the rotor blade arrives at the blade tip timing sensor is arranged into a series of data points according to the snapshot time sequence to obtain the actual time series.

6. The method according to claim 1, characterized in that In step 2, the ideal time for the rotor blade to arrive at the blade tip timing sensor is expressed as: ; in, is the rotor blade serial number, is the blade tip timing sensor number, Indicates the number of circles, Indicates the shaft rotation frequency. Indicates The installation angle of the blade tip timing sensor, Indicates the serial number is The rotor blade installation angle.

7. The method according to claim 6, characterized in that The vibration displacement of the rotor blade is obtained by the following formula: ; in, is the rotor blade speed, is the radius of rotation, The time difference between the ideal time and the actual time when the rotor blade reaches the blade tip timing sensor.

8. The method according to claim 1, characterized in that In step 2, the ideal time for the rotor blade to arrive at the blade tip timing sensor is arranged into a series of data points in snapshot time order to obtain an ideal time series.

9. A blade tip timing signal time-frequency non-convex compressed sensing system, characterized in that: The system comprises: A blade tip timing sensor layout module, which is used to install blade tip timing sensors at circumferential positions of the rotor blade casing and obtain a time series of the rotor blades reaching the blade tip timing sensors; A vibration displacement calculation module, which is used to construct a multi-measurement snapshot matrix based on the time difference between the ideal time and the actual time when the rotor blade reaches the blade tip timing sensor, the rotor blade rotation frequency and the rotation radius; The rotor blade vibration parameter identification module is used to construct a multi-measurement vector time-frequency non-convex compressed sensing model based on a multi-measurement snapshot matrix.

10. The system according to claim 9, characterized in that The system also includes: a fault diagnosis module, which is used to solve a multi-measurement vector time-frequency non-convex compressed sensing model under an optimization-minimization framework to obtain a rotor blade vibration signal time-frequency diagram, and the rotor blade vibration signal time-frequency diagram is used to sense the rotor blade crack fault condition.

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