Leaf tip timing sensor layout optimization method based on compression covariance sampling

Abstract

A leaf tip timing sensor layout optimization method based on compression covariance sampling comprises the following steps: determining a frequency upper bound F of leaf tip timing signal spectrum analysis; determining the number N of virtual sensors according to the frequency upper bound F and the blade disc rotation frequency fr; a minimum sparse ruler with the length of # imgabs0 # is searched, and the condition that the minimum sparse ruler comprises all integer intervals of 0-# imgabs1 #, the number of elements in the minimum sparse ruler is the minimum, and # imgabs2 # is a symbol for rounding down; and according to the minimum sparse ruler and the number N of the virtual sensors, calculating the installation angle of the blade tip timing sensor to determine the layout of the blade tip timing sensor.

Description

Technical Field

[0001] The present invention relates to the technical field of non-contact measurement of rotor blade vibration, and particularly to an optimization method for the layout of tip-timing sensors based on compressive covariance sampling. Background Art

[0002] The rotor blade is one of the key components of aero-engines and gas turbines. Due to harsh working environments such as high pressure, high temperature, and high rotational speed, the blades are prone to failure. Minor failures will further deteriorate over working time, leading to serious failures such as blade chunk shedding and fracture, resulting in the failure of aero-engine and gas turbine equipment and even causing safety accidents. Therefore, it is necessary to perform online monitoring of rotor blades to detect early failures in a timely manner.

[0003] The tip-timing technology is a newly emerging tip vibration measurement technology. Due to its non-contact and high-efficiency characteristics, tip-timing is considered applicable to measuring the vibration of rotating blades of equipment such as aero-engines, and then monitoring the health status of the blades. The tip-timing technology records the time when the blade reaches the sensor through sensors installed on the stationary casing to invert the tip displacement. In the absence of noise, the expected arrival time of the blade can be calculated through rotational speed and relative angle; the difference between the actual arrival time and the expected arrival time multiplied by the linear velocity can obtain the tip vibration displacement. Vibration parameters of the blade such as frequency and amplitude are important parameters for evaluating the blade health. Accurately identifying vibration parameters and even reconstructing the vibration spectrum from the displacement signal collected by tip-timing (abbreviated as tip-timing signal) is crucial for blade health monitoring and blade life prediction. However, the installation of tip-timing sensors is usually restricted by factors such as the structure and operation requirements of aero-engines. Therefore, tip-timing signals are usually severely undersampled, which results in the failure of traditional parameter identification methods and spectrum reconstruction methods. In order to recover the spectrum and identify parameters from severely undersampled signals, it is necessary to optimize the layout of a limited number of tip-timing sensors to measure as rich information as possible and improve the accuracy of spectrum reconstruction and parameter identification.

[0004] The above information disclosed in the background art section is only used to enhance the understanding of the background of the present invention, and thus may include information that does not constitute the prior art known to those of ordinary skill in the art. Summary of the Invention

[0005] The present invention provides an optimization method for the layout of tip-timing sensors based on compressive covariance sampling, which is used to recover the covariance information of the tip vibration signal, and then can achieve power spectrum reconstruction and vibration parameter identification of the tip vibration signal using as few sensors as possible. In addition, the present invention improves the acquisition efficiency of the sensor for the tip vibration signal and avoids information redundancy.

[0006] An optimization method for the layout of tip-timing sensors based on compressive covariance sampling includes:

[0007] Step 1: Determine the upper frequency bound F for the spectral analysis of the tip-timing signal.

[0008] Step 2: Determine the number N of virtual sensors according to the upper frequency bound F and the rotational frequency f of the disk. r Determine the number N of virtual sensors.

[0009] Step 3: Search for the minimum sparse ruler with a length of The conditions it satisfies are: the minimum sparse ruler contains all integer intervals from 0 to and the number of elements in the minimum sparse ruler is the least, is the floor function symbol;

[0010] Step 4: Calculate the installation angles of the tip-timing sensors according to the minimum sparse ruler and the number N of virtual sensors to determine the layout of the tip-timing sensors.

[0011] In the optimization method for the layout of tip-timing sensors based on compressive covariance sampling, in Step 1, according to the prior information D of the blade frequency, determine the upper frequency bound F for the spectral analysis of the tip-timing signal, , where is a coefficient greater than 0 to ensure that the upper frequency bound F is greater than the natural frequency of the blade to be measured.

[0012] In the optimization method for the layout of tip-timing sensors based on compressive covariance sampling, based on the finite element simulation analysis results of the blade model or determine the strain gauge modal analysis results to determine the prior information D of the blade frequency, is 0.2.

[0013] In the optimization method for the layout of tip-timing sensors based on compressive covariance sampling, in Step 2,

[0014] The number N of virtual sensors is

[0015] ,

[0016] where is the ceiling function symbol, and the number N of virtual sensors is the smallest integer not less than .

[0017] In the optimization method for the layout of tip-timing sensors based on compressive covariance sampling, in Step 3, the mathematical model of the minimum sparse ruler is as follows:

[0018] (1),

[0019] where Represents a sparse ruler, which is a set of integers, Represents the set Of the basis, that is, the set The number of elements in, Is a set containing all integers from 0 to All integers, Is the floor symbol, Is less than The largest integer, Is The difference set of, which is equal to the elements composed of the absolute values of the differences of the elements in any two. The mathematical definition is as follows:

[0020] ,

[0021] Where And Represents Any two elements in, And Can have the same or different values, Represents The absolute value of. Find a set That satisfies equation (1), denoted as Where M represents The number of elements in, and the minimum sparse ruler with length Is determined by traversal search based on equation (1).

[0022] In the method for optimizing the layout of tip-timing sensors based on compressive covariance sampling described above, in step 4,

[0023] The installation angle of the tip-timing sensor is:

[0024] ,

[0025] Where Represents the angle of the i-th sensor relative to the first tip-timing sensor in the positive direction of the blade disk rotation direction,

[0026] Install the first tip-timing sensor, and based on this, according to the calculated , install the 2nd to Mth tip-timing sensors to finally obtain an optimized layout of tip-timing sensors.

[0027] In the method for optimizing the layout of tip-timing sensors based on compressive covariance sampling described above, the blade disk is an integral titanium alloy blade disk with 18 blades.

[0028] Compared with the prior art, the present invention has the following advantages: The present invention uses compressive sampling to reduce the data sampling, transmission, and storage costs of structural health monitoring. The present invention is an efficient signal undersampling scheme and spectrum recovery method, which can realize the spectrum reconstruction of undersampled signals, and then can realize frequency and amplitude identification, optimize the layout of tip-timing sensors, and has fast and stable operation, is simple and feasible, and can realize the efficient storage and spectrum recovery of signals. BRIEF DESCRIPTION OF THE DRAWINGS

[0029] By reading the following detailed description of the preferred embodiments, various other advantages and benefits of the present invention will become clear to those of ordinary skill in the art. The accompanying drawings in the specification are only for the purpose of showing the preferred embodiments and are not considered to be a limitation of the present invention. Obviously, the following described drawings are only some embodiments of the present invention. For those of ordinary skill in the art, without creative efforts, other drawings can be obtained based on these drawings. Moreover, throughout the drawings, the same reference numerals are used to represent the same components.

[0030] In the drawings:

[0031] Figure 1 is a flowchart of the method for optimizing the layout of tip-timing sensors based on compressive covariance sampling proposed by the present invention;

[0032] Figure 2 is a schematic diagram of the finite element modal simulation analysis results of the blade;

[0033] Figure 3 is a schematic diagram of the optimized sensor layout according to the method of the present invention;

[0034] Figure 4 is a schematic diagram of the displacement data collected using the optimized layout;

[0035] Figure 5 is a schematic diagram of the covariance samples recovered from the signal samples;

[0036] Figure 6 is a schematic diagram of the power spectrum obtained by discrete Fourier transform of the covariance data.

[0037] The present invention will be further explained below in conjunction with the drawings and embodiments. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0038] The specific embodiments of the present invention will be described in more detail below with reference to the drawings. Although the specific embodiments of the present invention are shown in the drawings, it should be understood that the present invention can be implemented in various forms and should not be limited by the embodiments set forth herein. On the contrary, these embodiments are provided so that the present invention can be more thoroughly understood and the scope of the present invention can be fully communicated to those skilled in the art.

[0039] It should be noted that certain terms are used in the specification and claims to refer to specific components. Those skilled in the art should understand that technicians may use different terms to refer to the same component. The specification and claims do not distinguish components by the difference in terms, but by the difference in the functions of the components. For example, the terms "comprising" or "including" mentioned throughout the specification and claims are open-ended terms and should be interpreted as "including but not limited to". The subsequent description in the specification is for the purpose of describing the preferred embodiments of the present invention, but it is not intended to limit the scope of the present invention. The scope of protection of the present invention shall be determined by the appended claims.

[0040] For the convenience of understanding the embodiments of the present invention, the following will further explain with specific embodiments in conjunction with the accompanying drawings, and the accompanying drawings do not constitute a limitation to the embodiments of the present invention.

[0041] As Figures 1 to 6 shown, the method for optimizing the layout of tip-timing sensors based on compressive covariance sampling includes the following steps:

[0042] Step 1, determining the upper frequency bound F of the spectral analysis of the tip-timing signal;

[0043] Step 2, determining the number N of virtual sensors according to the upper frequency bound F and the rotational frequency f of the disk r of the blade;

[0044] Step 3, finding the minimum sparse ruler with a length of , and the conditions it satisfies are: the minimum sparse ruler contains all integer intervals from 0 to , and the number of elements in the minimum sparse ruler is the least, where

[0045] is the floor function symbol;

[0046] In the preferred embodiment of the method for optimizing the layout of tip-timing sensors based on compressive covariance sampling, in step 1, according to the prior information D of the blade frequency, the upper frequency bound F of the spectral analysis of the tip-timing signal is determined, , where is a coefficient greater than 0 to ensure that the upper frequency bound F is greater than the natural frequency of the blade to be measured.

[0047] In the preferred embodiment of the method for optimizing the layout of tip-timing sensors based on compressive covariance sampling, based on the finite element simulation analysis results of the blade model or the modal analysis results of the strain gauges to determine the prior information D of the blade frequency, is 0.2.

[0048] In the preferred embodiment of the method for optimizing the layout of tip-timing sensors based on compressive covariance sampling, in step 2,

[0049] The number N of virtual sensors is

[0050] ,

[0051] where is the ceiling symbol, and the number N of virtual sensors is the smallest integer not less than of.

[0052] In the preferred embodiment of the method for optimizing the layout of tip-timing sensors based on compressive covariance sampling, in step 3, the mathematical model of the minimum sparsity ruler is as follows:

[0053] (1),

[0054] where represents the sparsity ruler, which is a set of integers, represents the basis of the set , that is, the number of elements in the set , is a set containing all integers from 0 to , is the floor symbol, is less than of the largest integer, is the difference set of, which is equal to the elements composed of the absolute values of the differences of the elements in any two, and the mathematical definition is as follows:

[0055] ,

[0056] where and represent any two elements in, and can take the same value or different values, represents the absolute value of. Find a set that satisfies equation (1), denoted as , where M represents the number of elements in, and the length is The minimum sparse ruler is determined by traversal search based on Equation (1).

[0057] In a preferred embodiment of the method for optimizing the layout of tip-timing sensors based on compressive covariance sampling, in step 4,

[0058] The installation angle of the tip-timing sensor is:

[0059] ,

[0060] where represents the angle of the i-th sensor relative to the first tip-timing sensor with the positive direction of the blade disk rotation direction,

[0061] Install the first tip-timing sensor, and based on this, according to the calculated , install the 2nd to Mth tip-timing sensors, and finally obtain the optimized layout of the tip-timing sensors.

[0062] In a preferred embodiment of the method for optimizing the layout of tip-timing sensors based on compressive covariance sampling, the blade disk is an integral titanium alloy blade disk with 18 blades.

[0063] A system for optimizing the layout of tip-timing sensors includes,

[0064] A frequency upper bound generation unit that determines the frequency upper bound F for the spectral analysis of the tip-timing signal;

[0065] A virtual sensor number calculation unit that determines the number N of virtual sensors according to the frequency upper bound F and the blade disk rotation frequency f r to determine the number N of virtual sensors;

[0066] A minimum sparse ruler determination unit that searches for a minimum sparse ruler of length which satisfies the conditions that the minimum sparse ruler contains all integer intervals from 0 to and the number of elements in the minimum sparse ruler is the least, is the floor symbol;

[0067] A layout generation unit that calculates the installation angles of the tip-timing sensors according to the minimum sparse ruler and the number N of virtual sensors to determine the layout of the tip-timing sensors.

[0068] A computer storage medium, the storage medium includes computer instructions, when it runs on a computer, it causes the computer to execute the method described above.

[0069] An electronic device, the electronic device includes:

[0070] A memory, a processor, and a computer program stored on the memory and executable on the processor, where,

[0071] When the processor executes the program, the method described above is implemented.

[0072] In one embodiment, the method includes the following steps:

[0073] 1. Determine the upper frequency bound F of the spectrum analysis of the tip timing signal;

[0074] In this exemplary example, the tip timing technology is used to measure the tip vibration of a titanium alloy blisk. The titanium alloy blisk contains 18 blades and the blisk diameter is 196 mm. Three-dimensional modeling of the blisk is performed, and finite element analysis is carried out on it. According to the modal analysis results, the prior natural frequency of the blade is 850 Hz, as Figure 2 shown. To ensure that the upper frequency bound F of the spectrum analysis is greater than the natural frequency of the actual blade to be measured, take , where is a coefficient greater than 0. Here, take 0.2. Therefore, Hz.

[0075] 2. Determine the number N of virtual sensors according to the upper frequency bound F and the blisk rotation frequency f r ;

[0076] In this exemplary example, the rotation frequency of the blisk is 158 Hz, and the number of virtual sensors can be calculated:

[0077]

[0078] 3. Find the minimum sparse ruler with a length of , and the conditions to be met are: the sparse ruler contains all integer intervals from 0 to , and the number of elements in the sparse ruler is the least;

[0079] In this example, N = 13, , so it is necessary to find the minimum sparse ruler with a length of 6, and the conditions that the sparse ruler needs to meet are:

[0080] (1)

[0081] is the difference set of, which is equal to the set composed of the absolute values of the differences of the elements in any two. The mathematical definition is as follows:

[0082]

[0083] contains all integers from 0 to 6. According to the definition of, needs to meet , where C is the symbol for combination operation, ,! represents factorial operation, so .

[0084] The brute-force search algorithm starts from and traverses all possible value cases of to find the cases that satisfy the constraint condition . If, for all possible value cases of S, the constraint condition is not satisfied, let increase by 1, and then repeat the above steps until a case that satisfies the constraint condition is found . In this example, in the cases of and , a set of values that satisfy can be found, . is the set of integers that can be found to satisfy the constraint conditions and , and contains the fewest elements. Therefore is the minimum sparse ruler of length 6.

[0085] The minimum linear sparse ruler of length 6 can also be obtained by querying the typical minimum sparse ruler table. The typical minimum sparse ruler table

[0086]

[0087] 4. Calculate the installation angle of the sensor according to the minimum sparse ruler and N, and then determine the layout of the tip-timing sensors;

[0088] Therefore, the angle of the installed angle sensor can be calculated by the following formula

[0089]

[0090] where represents the angle of the i-th sensor relative to the first sensor, with the positive direction being the rotation direction of the blade disk, is the i-th element in.

[0091] In this exemplary example, the obtained minimum sparse ruler is , N = 13, so the angles of 4 sensors are calculated as {0°, 30°, 120°, 180°}. Therefore, when actually arranging the tip-timing sensors, select any appropriate position to install the first sensor, and take this as 0°, then install the 2nd - 4th sensors at the places with included angles of 30°, 120°, and 180° respectively. Thus, the optimized tip-timing sensor layout is determined. This optimized layout can be used to recover the covariance information of the tip vibration signal, and further, the power spectrum reconstruction and vibration parameter identification of the tip vibration signal can be realized.

[0092] The present invention proposes an optimized design method for tip-timing sensor layout based on compressive covariance sampling. This optimized layout can be used to recover the covariance information of the tip vibration signal, and further, the power spectrum reconstruction and vibration parameter identification of the tip vibration signal can be realized using as few sensors as possible. In addition, the present invention improves the acquisition efficiency of the sensor for the tip vibration signal and avoids information redundancy.

[0093]

Application Example

[0094] In this example, the tip-timing technology is used to measure the tip vibration of a titanium alloy blisk. The present invention is used to optimize the tip-timing sensor layout, and based on the optimized layout, the covariance information of the tip vibration signal is recovered. Further, the power spectrum reconstruction and vibration parameter identification of the tip vibration signal can be realized using as few sensors as possible.

[0095] As shown in the tip-timing test bench, the fiber optic tip-timing sensor is fixed on the stationary casing, and the rotational speed f of the blisk r is set to 158 Hz. The blisk is an integral titanium alloy blisk with 18 blades, and the diameter of the blisk is 196 mm. Three-dimensional modeling is performed on the blisk, and then finite element analysis is carried out on it. According to the modal analysis results, as Figure 2 shown, the prior natural frequency of the blade is 850 Hz. To ensure that the upper frequency bound F of the spectral analysis is greater than the natural frequency of the actual blade to be measured, take , where is a coefficient greater than 0. Here, take 0.2. Therefore Hz.

[0096] According to the upper frequency bound F and the rotational frequency f of the blisk r determine the number N of virtual sensors

[0097]

[0098] Then find the minimum sparse ruler with a length of , , and the conditions that this sparse ruler needs to meet are:

[0099] (1)

[0100] wherein is the difference set, which is equal to the elements composed of the absolute values of the differences of the elements in any two of them. The mathematical definition is as follows:

[0101]

[0102] contains all integers from 0 to 6. According to the definition, it can be known that needs to satisfy , where C is the combination operation symbol , and! represents the factorial operation. Therefore .

[0103] The brute-force search algorithm starts from and traverses all possible value-taking situations of to find the situation that satisfies the constraint condition . If at this time, all possible value-taking situations of S do not satisfy the constraint condition, let increase by 1, and then repeat the above steps until a set of that satisfies the constraint condition is found. In this example, in and cases, a set of values that satisfies can be found . is the integer set that can find to satisfy the constraint conditions and , and contains the fewest elements. Therefore is the minimum sparse ruler of length 6.

[0104] The minimum linear sparse ruler of length 6 can also be obtained by querying the said typical minimum sparse ruler table.

[0105] Finally, calculate the sensor installation angle according to the minimum sparse ruler and N

[0106]

[0107] where represents the angle of the i-th sensor relative to the first sensor, with the positive direction being the rotation direction of the blade disc is the i-th element in

[0108] In this exemplary example, the obtained minimum sparse ruler is , N = 12. Therefore, the angles of 4 sensors are calculated as {0°, 30°, 120°, 180°}. Therefore, when actually arranging the tip-timing layout, select any suitable position to install the first sensor, and take this as 0°, then install the second to fourth sensors at the places with included angles of 30°, 120°, and 180° respectively. Thus, the optimized tip-timing sensor layout is determined. This optimized layout can be used to recover the covariance information of the tip vibration signal, and further the power spectrum reconstruction and vibration parameter identification of the tip vibration signal can be realized.

[0109] Using this layout as Figure 2 shown to collect the tip vibration. The signal samples obtained by the 4 sensors are as Figure 3 shown. Then, calculate the equal covariance samples according to the collected signal samples, and the obtained covariance samples are as Figure 4 shown. Perform discrete Fourier transform on this covariance sample, and the power spectrum is obtained, as Figure 5 shown. From the power spectrum, it can be seen that the natural frequency of the blade is 866.6 Hz, and its power amplitude is 1.585×10 -6 mm 2 / Hz.

[0110] The present invention proposes an optimized design method for the tip-timing sensor layout based on compressed covariance sampling. This optimized layout can be used to recover the covariance information of the tip vibration signal, and further the power spectrum reconstruction and vibration parameter identification of the tip vibration signal can be realized using as few sensors as possible. In addition, the present invention improves the acquisition efficiency of the sensor for the tip vibration signal and avoids information redundancy.

[0111] Although the embodiments of the present invention have been described above in conjunction with the accompanying drawings, the present invention is not limited to the above specific embodiments and application fields. The above specific embodiments are merely illustrative and guiding, rather than restrictive. Those of ordinary skill in the art can also make many forms under the inspiration of this specification and without departing from the scope protected by the claims of the present invention, and these all belong to the scope of protection of the present invention.

Claims

1. A blade tip timing sensor layout optimization method based on compressed covariance sampling, characterized in that: The steps include: Step (1), determining the frequency upper bound F of the blade tip timing signal spectrum analysis; Step (2), according to the frequency upper limit F and the blade rotation frequency f r Determine the number of virtual sensors N; Step (3), find the length The minimum sparse ruler of , which satisfies the following conditions: the minimum sparse ruler contains 0~ All integer intervals of , and the minimum sparse ruler has the least number of elements, is the floor symbol; Step (4), calculating the blade tip timing sensor installation angle according to the minimum sparseness rule and the number of virtual sensors N, so as to determine the blade tip timing sensor layout.

2. The blade tip timing sensor layout optimization method based on compressed covariance sampling according to claim 1 is characterized in that: Preferably, in step (1), the frequency upper limit F of the spectrum analysis of the blade tip timing signal is determined according to the blade frequency prior information D. ,in, It is a coefficient greater than 0 to ensure that the upper frequency limit F is greater than the natural frequency of the blade to be measured.

3. The blade tip timing sensor layout optimization method based on compressed covariance sampling according to claim 2 is characterized in that: Based on the finite element simulation analysis results of the blade model or the strain gauge modal analysis results, the blade frequency prior information D is determined. is 0.

2.

4. The blade tip timing sensor layout optimization method based on compressed covariance sampling according to claim 1, characterized in that: In the step (2), The number of virtual sensors N is ， in is the round-up symbol, and the number of virtual sensors N is not less than The smallest integer.

5. The blade tip timing sensor layout optimization method based on compressed covariance sampling according to claim 4 is characterized in that: In step (3), the mathematical model of the minimum sparseness scale is as follows: (1)， in represents the sparse ruler, which is a set of integers, Representing a collection The basis of The number of elements in , is a string containing 0 to The set of all integers, is the floor symbol, is less than The largest integer, for The difference set of , which is equal to the element consisting of the absolute value of the difference between any two elements in , is mathematically defined as follows: ， in and express Any two elements in and The values ​​of can be the same or different. express The absolute value of , find a set that satisfies equation (1) , denoted as , where M represents The number of elements in , the length is The minimum sparseness scale of is determined by traversal search based on equation (1).

6. The blade tip timing sensor layout optimization method based on compressed covariance sampling according to claim 5, characterized in that: In the step (4), The blade tip timing sensor installation angle is: ， in represents the angle of the i-th sensor relative to the first blade tip timing sensor with the blade disk rotation direction as the positive direction, Install the first blade tip timing sensor and use it as a reference. , install the 2nd to Mth blade tip timing sensors, and finally obtain the optimized blade tip timing sensor layout.

7. The blade tip timing sensor layout optimization method based on compressed covariance sampling according to claim 1, characterized in that: The blisk is an 18-blade integral titanium alloy blisk.

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