CN113565585A - Method for extracting natural frequency of variable-working-condition rotating blade of single-blade-end timing sensor - Google Patents

Method for extracting natural frequency of variable-working-condition rotating blade of single-blade-end timing sensor Download PDF

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CN113565585A
CN113565585A CN202111017895.6A CN202111017895A CN113565585A CN 113565585 A CN113565585 A CN 113565585A CN 202111017895 A CN202111017895 A CN 202111017895A CN 113565585 A CN113565585 A CN 113565585A
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frequency
blade
sequence
index
data
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CN113565585B (en
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杨志勃
曹佳辉
陈雪峰
李浩琪
田绍华
王增坤
李文博
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Xian Jiaotong University
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    • F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F01—MACHINES OR ENGINES IN GENERAL; ENGINE PLANTS IN GENERAL; STEAM ENGINES
    • F01D—NON-POSITIVE DISPLACEMENT MACHINES OR ENGINES, e.g. STEAM TURBINES
    • F01D21/00—Shutting-down of machines or engines, e.g. in emergency; Regulating, controlling, or safety means not otherwise provided for
    • F01D21/003—Arrangements for testing or measuring
    • F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F01—MACHINES OR ENGINES IN GENERAL; ENGINE PLANTS IN GENERAL; STEAM ENGINES
    • F01D—NON-POSITIVE DISPLACEMENT MACHINES OR ENGINES, e.g. STEAM TURBINES
    • F01D25/00—Component parts, details, or accessories, not provided for in, or of interest apart from, other groups

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Abstract

The invention discloses a method for extracting the natural frequency of a variable working condition rotating blade of a single-blade-end timing sensor, which comprises the steps of acquiring the time pulse of the rotating blade by using the single-blade-end timing sensor, firstly converting the time pulse into a rotating speed, and then converting the actual reaching time and the theoretical reaching time difference delta t into displacement data according to the radius R and the rotating speed n of the blade; obtaining a sampling frequency-aliasing frequency graph with consistent aliasing frequency resolution by using a variable window length short-time Fourier transform or least square estimation equal frequency spectrum analysis method; extracting the characteristics of a sampling frequency-aliasing frequency diagram through Hough transformation or Radon transformation; comparing the extracted slope of the straight line with a rounding result, and calculating a reliability weight; and carrying out weighted average on the intercept estimation results of all the straight lines in the graph according to the credibility weight to obtain an estimated value of the natural frequency.

Description

Method for extracting natural frequency of variable-working-condition rotating blade of single-blade-end timing sensor
Technical Field
The invention belongs to the field of nondestructive testing of blades, and particularly relates to a method for extracting natural frequency of a variable-working-condition rotating blade of a timing sensor with a single blade end.
Background
Turbomachines are widely used in the industrial field, in particular in the fields of aviation, navigation and electrical energy. The blades are important parts of the turbomachinery for their respective functions, but due to their long-term impact with fluids and the great centrifugal forces, and also to the contingencies such as foreign body fragments, the integrity of the blades and the safety of the turbomachinery are threatened. Blade condition detection is therefore important to the user.
The traditional contact type measuring method, such as strain gauge measurement, is time-consuming, short in service life and low in efficiency, and is difficult to apply to an actual industrial environment, the Blade end Timing (BTT) is a non-contact type method, a probe (a capacitance type, an optical fiber type, an electric eddy current type and the like) installed in a static casing is used for recording the reaching time pulse of a Blade, and the difference between the theoretical reaching time and the actual reaching time without considering the vibration condition of the Blade is converted into the Blade end displacement, so that the vibration displacement of the tail end of the Blade is obtained. From this vibrational displacement, the health of the blade is analyzed. The natural frequency is a very effective index in fault diagnosis, the health condition of the blade can be reflected in the natural frequency of the blade, but the sampling rate of the blade end timing signal is related to the rotating speed and the number of sensors, and the sampling rate and the rotating speed are limited in practice, so that the blade end timing signal is a severely undersampled signal. The frequency is identified from the undersampled signals by means of a linear signal processing method, the traditional methods such as compressed sensing and multi-signal classification all need a plurality of leaf-end timing sensors, the installation angle of the sensors is required, the operation is complex, the time consumption is long, and the installation position of the sensors is limited in practical situations, so that the method based on the multi-leaf-end timing sensors fails, and the method is an important reason for the fact that the leaf-end timing technology cannot be applied to important equipment. Therefore, it is necessary to provide a blade-end timing signal blade frequency extraction method which uses fewer blade-end timing sensors and performs more efficient operation.
Disclosure of Invention
In view of the above, the present invention provides a method for extracting a natural frequency of a variable-condition rotating blade of a single-blade-end timing sensor, which is used for acquiring the natural frequency from severely undersampled blade-end timing data to realize health monitoring of the blade.
In order to realize the purpose, the invention adopts the following technical scheme:
a method for extracting the natural frequency of the variable working condition rotating blade of a single-blade-end timing sensor comprises the following steps,
the method comprises the steps that firstly, a single-blade end timing sensor is used for obtaining time pulse of a rotating blade, the rotating speed n of the rotating blade is generated based on the time pulse, and the difference delta t between actual reaching time and theoretical reaching time is converted into displacement data according to the blade radius R and the rotating speed n of the rotating blade;
secondly, obtaining a sampling frequency-aliasing frequency graph with consistent aliasing frequency resolution based on the displacement data by using a variable window length short-time Fourier transform or least square estimation isochronous frequency analysis method;
thirdly, extracting characteristics of a sampling frequency-aliasing frequency diagram through Hough transformation or Radon transformation, wherein the characteristics comprise a straight slope and an intercept;
a fourth step of rounding the slope of the straight line to obtain a rounding result, and comparing the rounding result with the slope of the straight line to calculate the reliability;
and fifthly, carrying out weighted average on intercepts of all straight lines in the sampling frequency-aliasing frequency diagram according to the credibility to obtain an estimated value of the natural frequency.
In the method for extracting the natural frequency of the variable working condition rotating blade of the single-blade-end timing sensor, in the first step, the single-blade-end timing sensor is used for collecting the time pulse t of the rotating blade under the condition of variable rotating speed, the rotating speed is calculated by utilizing the two time reaching time pulses of the same rotating blade,
Figure BDA0003240134770000021
wherein n (p) represents the average rotation speed of the p-th circle in revolutions per minute, ti pWhich represents the time, in seconds, that the ith vane reaches the sensor at the p-th turn,
Figure BDA0003240134770000022
indicating the time at which the ith vane reaches the sensor at circle p-1,
Figure BDA0003240134770000023
indicating the time in seconds for the ith vane to reach the sensor at circle p + 1.
The ideal arrival time is the time at which the blade reaches the sensor without vibration
Figure BDA0003240134770000024
Figure BDA0003240134770000031
Wherein
Figure BDA0003240134770000032
Represents the ideal time, θ, for the ith blade to reach the sensor at the p-th turniRepresenting the angle of the ith blade, alpha representing the installation angle of the sensor, and the displacement data is
Figure BDA0003240134770000033
Wherein
Figure BDA0003240134770000034
Denotes the ith blade at
Figure BDA0003240134770000035
The displacement of the moment.
In the method for extracting the natural frequency of the variable working condition rotating blade of the single-blade-end timing sensor, in the second step, when the short-time Fourier transform of the variable window length is carried out, the step length delta f of the sampling frequency is setsAnd generating a sampling frequency sequence according to the rotating speed to determine the position center position of the short-time Fourier window:
Figure BDA0003240134770000036
which is composed of
Figure BDA0003240134770000037
Representing the lower bound of the selected analyzed speed range. a is an integer representing FsNumber of middle elements, i.e. sequence FsThe value of a satisfies:
Figure BDA0003240134770000038
Figure BDA0003240134770000039
representing an upper bound of the selected analyzed speed range.
Figure BDA00032401347700000310
Wherein f isrRepresenting the collected speed vector, h1，h2The upper and lower limit of the rotation speed analysis range is artificially set as an overrun-preventing threshold;
setting alias frequency resolution Δ RfAnd calculating the window length of each short-time Fourier window according to the rotating speed:
Figure BDA00032401347700000311
wherein N isL(m) denotes the window length of the mth window, i.e. the length of the data participating in the Fourier transform, Fs(m) denotes the m-th sequence of sampling frequencies, i.e. the sampling frequency of the m-th window position [. ]]oddRepresenting operations taking an odd number of data nearbyIn the calculation, the calculation is carried out,
and calculating the data index which is actually closest to the sampling frequency according to the sampling frequency of the ideal window center:
Figure BDA0003240134770000041
wherein
Figure BDA0003240134770000042
The index value which makes the post formula get the minimum value is obtained, r is the acquired frequency conversion data, one frequency conversion is obtained in each circle, so frIs a frequency vector, fr(index) represents frThe middle index element value.
Taking the data index iindex as an intercepting data center and the window length NL(m) as data length, intercepting the displacement data y [ index- (N)L(m)-1)/2：index+(NL(m)-1)/2]Performing fast Fourier transform (displacement data y [ index- (N))L(m)-1)/2：index+(NL(m)-1)/2]What is meant is
Figure BDA0003240134770000043
Where y (n) is the sampled signal, i is an imaginary symbol,
Figure BDA0003240134770000044
n is the length of the acquired signal, the number of elements in y, N is an iteration number, from index- (N)L(m) -1)/2 traversal to index + (N)L(m) -1)/2, i.e., all elements in pass y, k is an integer from 0 to N-1, and y (k) represents the kth data after discrete fourier transform.
Setting alias frequency resolution Δ RfGenerating an aliased frequency sequence Fn：
Figure BDA0003240134770000045
Generating an amplitude matrix Aa×bWhere a is the aliasing frequency sequence length, b is the sampling frequency sequence length,
storing the absolute value of the Fourier transform result of the data in the mth window into an amplitude matrix Aa×bIn the m-th column in (1), all windows are traversed by the same analogy,
according to the central position FsAlias frequency sequence FhAnd amplitude matrix Aa×bA sampling frequency-aliasing frequency graph is plotted, and round (·) represents a rounding operation.
In the method for extracting the natural frequency of the variable working condition rotating blade of the single-blade-end timing sensor, in the second step,
based on aliasing frequency resolution Δ RfAnd a sampling frequency step Δ fsTo obtain
Figure BDA0003240134770000051
Figure BDA0003240134770000052
Wherein
Figure BDA0003240134770000053
Respectively representing the lower and upper bounds of the selected analyzed speed range, round (-) representing rounding,
calculating a window length sequence:
Figure BDA0003240134770000054
wherein represents NL(m) the window length of the mth window, i.e. the length of data participating in the Fourier transform, Fs(m) denotes the m-th sequence of sampling frequencies, i.e. the sampling frequency of the m-th window position [. ]]oddRepresenting an operation taking an odd number of data nearby,
calculating the data index actually closest to the sampling frequency based on the sampling frequency of the ideal window center:
Figure BDA0003240134770000055
wherein
Figure BDA0003240134770000056
The index value of the post formula to the minimum value is obtained, the data index is taken as a data interception center, and N is usedL(m) as data length, intercepting the displacement data y [ index- (N)L(m)-1)/2：index+(NL(m)-1)/2]Performing least square estimation to obtain amplitude coefficient by the following formula
Figure BDA0003240134770000057
Wherein QkIs a two-dimensional matrix composed of sine sequences and cosine sequences, the number of columns is 2,
Figure BDA0003240134770000058
is a two-dimensional matrix with 2 columns, and two values of each row are squared and then rooted to obtain an amplitude estimate AkY is the blade displacement, which is expressed as follows:
Figure BDA0003240134770000059
，Qk＝[cksk]，y＝[y(index-(NL(m)-1)/2)，y(index-(NL(m)-1)/2+1)，…，y(index+(NL(m)-1)/2)]，
Figure BDA00032401347700000510
taking the value of k from 1 to a to obtain Am＝[A1，a2，…，Aa]The amplitude result A of least square estimation of the data in the mth windowmFilling into the two-dimensional matrix Aa×bWhen all windows are operated as above, the two-dimensional matrix A is obtaineda×bAccording to Fs，Fn，Aa×bPlotting a sampling frequency-aliased frequency map, wherein FsFor sampling a sequence of frequencies, FhFor aliasing of frequency sequences, Aa×bIs a two-dimensional amplitude matrix.
In the method for extracting the natural frequency of the variable-working-condition rotating blade of the single-blade-end timing sensor, in the third step, an angle step delta theta and a distance step delta L of Hough transformation or Radon transformation are set to generate an angle sequence beta and a distance step sequence L:
β＝[-90°，-90°+Δθ，-90°+2Δθ，…，90°]，
Figure BDA0003240134770000061
Figure BDA0003240134770000062
wherein H, W are the width and height pixel sizes of the image, respectively, where LRDistance step sequence, L, representing Radon transformHAnd representing a distance step sequence of Hough transformation, and traversing the whole sampling frequency-aliasing frequency graph through the generated angle sequence beta and the distance step sequence L to realize feature extraction.
In the method for extracting the natural frequency of the variable working condition rotating blade of the single-blade-end timing sensor, in the third step,
the method comprises the following steps of (1) expressing a straight line in a sampling frequency-aliasing frequency graph as a peak value in a new space after Radon transformation or Hough transformation, extracting a peak value coordinate (beta, L), and obtaining a slope and an intercept based on the peak value coordinate (beta, L), wherein the slope and the intercept of the graph after Hough transformation are calculated by a formula:
Figure BDA0003240134770000063
Figure BDA0003240134770000064
slope and intercept calculation formula of graph after Radon transformation:
Figure BDA0003240134770000071
Figure BDA0003240134770000072
where β is the corresponding angular coordinate, L is the corresponding distance coordinate, round (.) represents a rounding operation, where H, W represents the width, height pixel size of the image, k represents the slope, c represents the intercept, a, b represent the sampling frequency sequence F, respectivelysAnd an aliased frequency sequence FnLength of (1), therefore Fs(a) Representing a sampling frequency sequence FsThe last element in (1), Fn(b) Representing an alias-taking frequency sequence FnThe last element in (1), Fs(1) Representing a sampling frequency sequence FsThe first element in (b), β, L are the abscissa and ordinate of the peak bright spot in Hough space (Radon space), respectively.
In the method for extracting the natural frequency of the variable working condition rotating blade of the single-blade-end timing sensor, in the fourth step,
the weight function for confidence is:
Figure BDA0003240134770000073
wherein wkA weight value representing a k-th line; k is a radical ofkRepresents the slope of the k-th line and q is the total number of lines in the sampling frequency-alias frequency diagram.
In the method for extracting the natural frequency of the variable working condition rotating blade of the single-blade-end timing sensor, in the fifth step, weighted average is carried out on intercept estimation results of all straight lines in a graph according to credibility weight:
Figure BDA0003240134770000074
wherein c isiRepresents the intercept of the ith line,
Figure BDA0003240134770000075
representing the natural frequency estimate.
The method does not need additional signal reconstruction and more blade end timing sensors, has a simple identification system, is quick and stable in operation, is simple and feasible, and can extract the natural frequency of the rotating blade by using the single-blade end timing sensor.
Drawings
The invention may best be understood by referring to the following description taken in conjunction with the accompanying drawings.
FIG. 1 is a schematic step diagram of a method for extracting natural frequency of a variable working condition rotating blade of a single-blade-end timing sensor according to an embodiment of the invention;
FIG. 2 is a schematic diagram of a single-blade-end timing sensor variable-condition rotating blade natural frequency identification test bed of the single-blade-end timing sensor variable-condition rotating blade natural frequency extraction method according to one embodiment of the invention;
FIG. 3 is a time domain diagram of blade end displacement of a blade 1 acquired by a single-blade-end timing sensor according to a variable working condition rotating blade natural frequency extraction method of the single-blade-end timing sensor in one embodiment of the present invention;
FIG. 4 is a sampling frequency-aliasing frequency diagram of the blade 1 obtained by variable window long-short time Fourier transform according to the variable working condition rotating blade natural frequency extraction method of the single-blade-end timing sensor in one embodiment of the invention;
FIG. 5 is a sampling frequency-aliasing frequency diagram of the blade 1 obtained by least square estimation according to the method for extracting the natural frequency of the variable working condition rotating blade of the single-blade-end timing sensor in the embodiment of the invention;
FIG. 6 is a sampling frequency-aliasing frequency diagram of the variable working condition rotating blade natural frequency extraction method of the single-blade-end timing sensor according to one embodiment of the invention, after low frequency components are removed;
FIG. 7 is a Hough transformation result diagram of a sampling frequency-aliasing frequency diagram of the variable working condition rotating blade natural frequency extraction method of the single-blade-end timing sensor according to one embodiment of the invention;
fig. 8 is a graph of a Radon transform result of a sampling frequency-aliasing frequency map of the variable working condition rotating blade natural frequency extraction method of the single-blade-end timing sensor according to one embodiment of the present invention.
Detailed Description
To more clearly illustrate the objects, aspects and advantages of the present invention, the present invention will now be described in further detail with reference to fig. 1 to 8 and an exemplary embodiment. It should be understood that the exemplary embodiments described herein are only for the purpose of illustrating the present invention and do not limit the applicable scope of the present invention.
The invention provides a method for extracting the natural frequency of a variable working condition rotating blade of a single-blade-end timing sensor, which comprises the following steps:
the method comprises the steps that firstly, a single-blade end timing sensor is used for obtaining time pulse of a rotating blade, the rotating speed n of the rotating blade is generated based on the time pulse, and the difference delta t between actual reaching time and theoretical reaching time is converted into displacement data according to the blade radius R and the rotating speed n of the rotating blade;
secondly, obtaining a sampling frequency-aliasing frequency graph with consistent aliasing frequency resolution based on the displacement data by using a variable window length short-time Fourier transform or least square estimation isochronous frequency analysis method;
thirdly, extracting characteristics of a sampling frequency-aliasing frequency diagram through Hough transformation or Radon transformation, wherein the characteristics comprise a straight slope and an intercept;
a fourth step of rounding the slope of the straight line to obtain a rounding result, and comparing the rounding result with the initial estimation value to calculate the reliability; the initial estimation value is an initial estimation value of a slope of a straight line, and is obtained by extracting features (straight line slope) of the straight line in a sampling frequency-aliasing frequency diagram through Hough transformation or Radon transformation.
And fifthly, carrying out weighted average on intercept estimation results of all straight lines in the sampling frequency-aliasing frequency diagram according to the credibility to obtain an estimated value of the natural frequency.
In the preferred embodiment of the method for extracting the natural frequency of the variable working condition rotating blade of the single-blade-end timing sensor, in the first step, the single-blade-end timing sensor is used for collecting the time pulse t of the rotating blade under the condition of variable rotating speed, the rotating speed is calculated by utilizing the two time reaching time pulses of the same rotating blade,
Figure BDA0003240134770000091
where n (p) denotes the average rotational speed of the p-th turn in revolutions per minute,
Figure BDA0003240134770000092
which represents the time, in seconds, that the ith vane reaches the sensor at the p-th turn,
Figure BDA0003240134770000093
indicating the time at which the ith vane reaches the sensor at circle p-1,
Figure BDA0003240134770000094
which represents the time, in seconds, at which the ith vane reaches the sensor at circle p +1,
the ideal arrival time is the time at which the blade reaches the sensor without vibration
Figure BDA0003240134770000095
Figure BDA0003240134770000096
Wherein
Figure BDA0003240134770000097
Represents the ideal time, θ, for the ith blade to reach the sensor at the p-th turniRepresenting the angle of the ith blade, alpha representing the installation angle of the sensor, and the displacement data is
Figure BDA0003240134770000101
Wherein
Figure BDA0003240134770000102
Denotes the ith blade at
Figure BDA0003240134770000103
The displacement of the moment.
In the preferred embodiment of the single-blade-end timing sensor variable-working-condition rotating blade common frequency extraction method, in the second step, during short-time Fourier transform with variable window length, the sampling frequency step length delta f is setsAnd generating a sampling frequency sequence according to the rotating speed to determine the position center position of the short-time Fourier window:
Figure BDA0003240134770000104
wherein
Figure BDA0003240134770000105
Representing the lower bound of the selected analyzed speed range. a is an integer representing FsNumber of middle elements, i.e. sequence FsThe value of a satisfies:
Figure BDA0003240134770000106
Figure BDA0003240134770000107
representing an upper bound of the selected analyzed speed range.
Figure BDA0003240134770000108
Wherein f isrRepresenting the collected speed vector, h1，h2The upper and lower limit of the rotation speed analysis range is artificially set as an overrun-preventing threshold;
setting alias frequency resolution Δ RfAnd calculating the window length of each short-time Fourier window according to the rotating speed:
Figure BDA0003240134770000109
wherein N isL(m) denotes the window length of the mth window, i.e. the length of the data participating in the Fourier transform, Fs(m) denotes the m-th sequence of sampling frequencies, i.e. the sampling frequency of the m-th window position [. ]]oddRepresenting an operation taking an odd number of data nearby,
and calculating the data index which is actually closest to the sampling frequency according to the sampling frequency of the ideal window center:
Figure BDA0003240134770000111
wherein
Figure BDA0003240134770000112
Denotes the index value, f, for finding the minimum value of the post equationrIs the acquired frequency conversion data, one frequency conversion is obtained for each turn, so frIs a frequency vector, fr(index) represents frThe middle index element value.
Taking the data index iindex as an intercepting data center and the window length NL(m) as data length, intercepting the displacement data y [ index- (N)L(m)-1)/2：index+(NL(m)-1)/2]Performing fast Fourier transform to represent the index- (N) of the displacement data (vector) yL(m) -1)/2 to index + (N)L(m) -1)/2 element values, namely, displacement data of a part of the displacement data is taken out.
Figure BDA0003240134770000113
Where y (n) is the sampled signal, i is an imaginary symbol,
Figure BDA0003240134770000114
n is the length of the acquired signal, the number of elements in y, N is an iteration number, from index- (N)L(m) -1)/2 traversal to index + (N)L(m) -1)/2, i.e., all elements in pass y, k is an integer from 0 to N-1, and y (k) represents the kth data after discrete fourier transform. (supplement meaning of yn, yk)
Setting alias frequency resolution Δ RfGenerating an aliased frequency sequence Fh：
Fh＝[0，ΔRf，2ΔRf，…，(b-1)ΔRf]Generating an amplitude matrix Aa×bWhere a is the aliasing frequency sequence length, b is the sampling frequency sequence length,
storing the absolute value of the Fourier transform result of the data in the mth window into an amplitude matrix Aa×bIn the m-th column in (1), all windows are traversed by the same analogy,
according to the central position FsAlias frequency sequence FnAnd amplitude matrix Aa×bA sampling frequency-aliasing frequency graph is plotted, and round (·) represents a rounding operation.
In the preferred embodiment of the method for extracting the natural frequency of the variable working condition rotating blade of the single-blade-end timing sensor, in the second step,
based on aliasing frequency resolution Δ RfAnd sampling frequencyStep size Δ fsTo obtain
Fh＝[0，ΔRf，2ΔRf，…，(b-1)ΔRf]，
Figure BDA0003240134770000121
Wherein
Figure BDA0003240134770000122
Respectively representing the lower and upper bounds of the selected analyzed speed range, round (-) representing rounding,
calculating a window length sequence:
Figure BDA0003240134770000123
wherein represents NL(m) the window length of the mth window, i.e. the length of data participating in the Fourier transform, Fs(m) denotes the m-th sequence of sampling frequencies, i.e. the sampling frequency of the m-th window position [. ]]addRepresenting an operation taking an odd number of data nearby,
calculating the data index actually closest to the sampling frequency based on the sampling frequency of the ideal window center:
Figure BDA0003240134770000124
wherein
Figure BDA0003240134770000125
The index value of the post formula to the minimum value is obtained, the data index is taken as a data interception center, and N is usedL(m) as data length, intercepting the displacement data y [ index- (N)L(m)-1)/2：index+(NL(m)-1)/2]Performing least square estimation to obtain amplitude coefficient by the following formula
Figure BDA0003240134770000126
Wherein QkIs a two-dimensional matrix composed of sine sequences and cosine sequences, the number of columns is 2,
Figure BDA0003240134770000127
is a two-dimensional matrix with 2 columns, and two values of each row are squared and then rooted to obtain an amplitude estimate AkY is the blade displacement, which is expressed as follows:
Figure BDA0003240134770000128
，Qk＝[ck sk]，
y＝[y(index-(NL(m)-1)/2)，y(index-(NL(m)-1)/2+1)，…，y(index+(NL(m)-1)/2)]
Figure BDA0003240134770000129
taking the value of k from 1 to a to obtain Am＝[A1，A2，…，Aa]The amplitude result A of least square estimation of the data in the mth windowmFilling into the two-dimensional matrix Aa×bWhen all windows are operated as above, the two-dimensional matrix A is obtaineda×bAccording to Fs，Fb，Aa×bAnd drawing a sampling frequency-aliasing frequency graph. In which F issFor sampling a sequence of frequencies, FnFor aliasing of frequency sequences, Aa×bIs a two-dimensional amplitude matrix.
In the preferred embodiment of the method for extracting the natural frequency of the variable working condition rotating blade of the single-blade-end timing sensor, in the third step, an angle step delta theta and a distance step delta L of Hough transformation or Radon transformation are set, and an angle sequence beta and a distance step sequence L are generated:
β＝[-90°，-90°+Δθ，-90°+2Δθ，…，90°]，
Figure BDA0003240134770000131
Figure BDA0003240134770000132
h, W are the width and height of the imageSize of element wherein LRDistance step sequence, L, representing Radon transformHAnd representing a distance step sequence of Hough transformation, and traversing the whole sampling frequency-aliasing frequency graph through the generated angle sequence beta and the distance step sequence L to realize feature extraction.
In the preferred embodiment of the method for extracting the natural frequency of the variable working condition rotating blade of the single-blade-end timing sensor, in the third step,
the method comprises the following steps of (1) expressing a straight line in a sampling frequency-aliasing frequency graph as a peak value in a new space after Radon transformation or Hough transformation, extracting a peak value coordinate (beta, L), and obtaining a slope and an intercept based on the peak value coordinate (beta, L), wherein the slope and the intercept of the graph after Hough transformation are calculated by a formula:
Figure BDA0003240134770000133
Figure BDA0003240134770000134
slope and intercept calculation formula of graph after Radon transformation:
Figure BDA0003240134770000135
Figure BDA0003240134770000141
where β is the corresponding angular coordinate, L is the corresponding distance coordinate, and round (·) represents a rounding operation. Y) wherein H, W are the width and height pixel size of the image, respectively, k represents the slope, c represents the intercept, and a, b represent the sampling frequency sequence F, respectivelysAnd an aliased frequency sequence FhLength of (1), therefore Fs(a) Representing a sampling frequency sequence FsThe last element in (1), Fh(b) Representing an alias-taking frequency sequence FhThe last element in (1). Beta, L are respectively the abscissa and ordinate of the peak bright spot in Hough space (Radon space)。
In the preferred embodiment of the method for extracting the natural frequency of the variable working condition rotating blade of the single-blade-end timing sensor, in the fourth step,
the weight function for confidence is:
Figure BDA0003240134770000142
wherein wkA weight value representing a k-th line; k is a radical ofkRepresents the slope of the k-th line and q is the total number of lines in the sampling frequency-alias frequency diagram.
In a preferred embodiment of the method for extracting the natural frequency of the variable working condition rotating blade of the single-blade-end timing sensor, in the fifth step, weighted averaging is performed on intercept estimation results of all straight lines in the graph according to the credibility weight:
Figure BDA0003240134770000143
wherein b isiRepresents the intercept of the ith line,
Figure BDA0003240134770000144
representing the natural frequency estimate.
In one embodiment, the method includes the steps of,
acquiring time pulse of a rotating blade by using a single-blade-end timing sensor, converting the time pulse into a rotating speed, and converting actual reaching time and theoretical reaching time difference delta t into displacement data according to the radius R of the blade and the rotating speed n;
obtaining a sampling frequency-aliasing frequency graph with consistent aliasing frequency resolution by using a variable window length short-time Fourier transform or least square estimation isochronous frequency analysis method;
the characteristics of the sampling frequency-aliasing frequency map, namely the slope and intercept of a straight line,
comparing the extracted slope of the straight line with a rounding result, and calculating a reliability weight;
and carrying out weighted average on the intercept estimation results of all the straight lines in the graph according to the credibility weight to obtain an estimated value of the natural frequency.
The invention provides a method for extracting the natural frequency of a variable working condition rotating blade of a single-blade-end timing sensor, which comprises the following steps:
(1) the method comprises the steps of acquiring time pulses of rotating blades by using a single-blade-end timing sensor, converting the time pulses into rotating speed, and converting actual reaching time and theoretical reaching time difference delta t into displacement data according to the radius R of the blades and the rotating speed n.
In the illustrative example, specifically, 1 optical fiber type blade end timing sensor is fixed on the casing, the initial rotating speed is set to be 100Hz, the rotating speed acceleration is 1Hz/s, and the rotating speed variation range is 99Hz-182 HzHz. The blisk is a 12-blade integral titanium alloy TC4 blisk, the radius of the blisk is 98mm, a single-blade-end timing sensor is used for acquiring the arrival time pulse of a rotating blade, the rotating speed of a rotating shaft is acquired, and the difference between the theoretical arrival time and the actual arrival time is converted into blade-end displacement according to the rotating speed and the length of the blade, as shown in figure 2.
(2) And obtaining a sampling frequency-aliasing frequency diagram with consistent aliasing frequency resolution by using a variable window length short-time Fourier transform or least square estimation isochronous frequency analysis method. The two methods only have difference on final amplitude estimation, and the previous sampling frequency sequence, aliasing frequency sequence and window length calculation part are the same.
In the present exemplary example, the frequency conversion range of the data of the selective analysis is 101Hz to 180Hz, the sampling frequency step is 0.5Hz, and the aliasing frequency step is 0.4Hz, thereby generating a sampling frequency sequence FsAnd an aliased frequency step sequence Fh：
Fs＝[101，101.5，102，…，180]1×167
Fh＝[0，0.4，0.8，…，90]1×231
Displacement of the 1 st window at 101Hz, window length is calculated:
Figure BDA0003240134770000161
and calculating the data index which is actually closest to the sampling frequency according to the sampling frequency of the ideal window center:
Figure BDA0003240134770000162
since the calculated index is 213, the index of the data in the first window is index- (N)L(1)-1)/2：index-(NL(1) 1)/2, i.e., 87 to 339.
When the window-variable long-short-time Fourier method is used, the data of y (87), y (88), … and y (339) are subjected to fast Fourier transform, and the amplitude is obtained as shown in formula 7.
When least squares estimation is used, the amplitude is obtained by 231 iterations, as shown in equation 13, to obtain amplitude information.
Filling the amplitude data obtained from the data in the first window into the two-dimensional matrix A231×167Column 1, and so on until the data magnitude transformation in the last window is completed.
According to Fs，Fn，A231×167A 3-dimensional sampling frequency-aliasing frequency map can be plotted, wherein fig. 4 is a sampling frequency-aliasing frequency map obtained by variable window long-short time fourier transform, and fig. 5 is a sampling frequency-aliasing frequency map obtained by least square estimation.
(3) Extraction of characteristics (slope and intercept of straight line) of sampling frequency-aliasing frequency map by Hough transform or Radon transform
In this example, the angle step Δ θ of the Hough transform or Radon transform is set to 0.1 ° and the distance step Δ L is set to 1, an angle sequence β and a distance sequence L are generated, a low frequency part in the sampling frequency-aliasing frequency map is removed, a map with aliasing frequencies of 4Hz to 91Hz is cut, and as shown in fig. 6, the wide and high pixel sizes of the obtained image are: w831, H680.
β＝[-90°，-90°+Δθ，-90°+2Δθ，…，90°]
LR＝[-537，-536，-535，…，536，537]
LH＝[-1074，-1073，-1072，…，1073，1074]
And (3) transforming the image with the aliasing frequency low-frequency part removed by using Hough transformation or Radon transformation, wherein FIG. 7 is a result of the Radon transformation, FIG. 8 is a result of the Hough transformation, and linear slopes and intercepts in the image after the Hough transformation and the Radon transformation are respectively calculated by formulas (17), (18), (19) and (20) according to the extracted peak value coordinates (shown in the figure).
TABLE 1 calculation of slope and intercept
Figure BDA0003240134770000171
(4) And comparing the slope of the extracted straight line with the rounding result, and calculating the reliability weight.
In the present exemplary example, the confidence weight is calculated from the results of table 1, the calculation expression is formula (21),
Figure BDA0003240134770000181
(5) and carrying out weighted average on the intercept estimation results of all the straight lines in the graph according to the credibility weight to obtain an estimated value of the natural frequency.
In this exemplary embodiment, the results of the Hough transform and Radon transform are weighted and summed, respectively, according to equation (22), resulting in: 884.06Hz and 881.20Hz, the blade was analyzed by using 5 sensors to collect its vibration displacement according to the modified Multiple Signal Classification (MUSIC) algorithm, resulting in a result of 883 Hz. This is very close to the blade frequency that this patent used the single-blade end timing sensor to obtain, and the error is within 3Hz, shows that this method is feasible, and Hough transform and Radon transform can both obtain similar result in addition, shows that Hough transform and Radon transform can both extract the straight line characteristic in sampling frequency-aliasing frequency diagram, all are applicable to this patent.
The method does not need additional signal reconstruction and more blade end timing sensors, has a simple identification system, is quick and stable in operation, is simple and feasible, and can extract the natural frequency of the rotating blade by using the single-blade end timing sensor.
[ application example ]
Fixing 1 optical fiber type blade end timing sensor on a casing, setting the initial rotating speed to be 100Hz, the rotating speed acceleration to be 1Hz/s, and setting the rotating speed within the range of 99Hz-182 HzHz. The blisk is a 12-blade integral titanium alloy TC4 blisk, the radius of the blisk is 98mm, a single-blade-end timing sensor is used for acquiring the arrival time pulse of a rotating blade, the rotating speed of a rotating shaft is acquired, and the difference between the theoretical arrival time and the actual arrival time is converted into blade-end displacement according to the rotating speed and the length of the blade, as shown in figure 2.
Selecting the frequency conversion range of the analyzed data to be 101Hz to 180Hz, the sampling frequency step size to be 0.5Hz, and the aliasing frequency step size to be 0.4Hz, thereby generating a sampling frequency sequence FsAnd an aliased frequency step sequence Fh：
Fs＝[101，101.5，102，…，180]1×167
Fh＝[0，0.4，0.8，…，90]1×231
Displacement of the 1 st window at 101Hz, window length is calculated:
Figure BDA0003240134770000191
and calculating the data index which is actually closest to the sampling frequency according to the sampling frequency of the ideal window center:
Figure BDA0003240134770000192
since the calculated index is 213, the index of the data in the first window is index- (N)L(1)-1)/2：index-(NL(1) 1)/2, i.e., 87 to 339.
When the window-variable long-short-time Fourier method is used, the data of y (87), y (88), … and y (339) are subjected to fast Fourier transform, and the amplitude is obtained as shown in formula 7.
When least squares estimation is used, the amplitude is obtained by 231 iterations, as shown in equation 13, to obtain amplitude information.
Filling the amplitude data obtained from the data in the first window into the two-dimensional matrix A231×167Column 1, and so on until the data magnitude transformation in the last window is completed.
According to Fs，Fn，A231×167A 3-dimensional sampling frequency-aliasing frequency map can be plotted, wherein fig. 4 is a sampling frequency-aliasing frequency map obtained by variable window long-short time fourier transform, and fig. 5 is a sampling frequency-aliasing frequency map obtained by least square estimation.
Setting the angle step length delta theta of the Hough transform or Radon transform to 0.1 degrees and the distance step length delta L to 1, generating an angle sequence beta and a distance sequence L, removing a low-frequency part in a sampling frequency-aliasing frequency graph, and intercepting a graph with aliasing frequency of 4 Hz-91 Hz, as shown in fig. 6, so as to obtain the wide and high pixel sizes of an image as follows: w831, H680.
β＝[-90°，-90°+Δθ，-90°+2Δθ，…，90°]
LR＝[-537，-536，-535，…，536，537]
LH＝[-1074，-1073，-1072，…，1073，1074]
And (3) transforming the image with the aliasing frequency low-frequency part removed by using Hough transformation or Radon transformation, wherein FIG. 7 is a result of the Radon transformation, FIG. 8 is a result of the Hough transformation, and linear slopes and intercepts in the image after the Hough transformation and the Radon transformation are respectively calculated by formulas (17), (18), (19) and (20) according to the extracted peak value coordinates (shown in the figure).
TABLE 1 calculation of slope and intercept
Figure BDA0003240134770000201
Figure BDA0003240134770000211
From the results of table 1, the confidence weights are calculated, the calculation expression is formula (21),
Figure BDA0003240134770000212
and (3) respectively carrying out weighted summation on the results of Hough transformation and Radon transformation according to a formula (22), wherein the obtained results are respectively as follows: 884.06Hz and 881.20Hz, the blade was analyzed by using 5 sensors to collect its vibration displacement according to the modified Multiple Signal Classification (MUSIC) algorithm, resulting in a result of 883 Hz. This is very close to the blade frequency that this patent used the single-blade end timing sensor to obtain, and the error is within 3Hz, shows that this method is feasible, and Hough transform and Radon transform can both obtain similar result in addition, shows that Hough transform and Radon transform can both extract the straight line characteristic in sampling frequency-aliasing frequency diagram, all are applicable to this patent.
The method does not need additional signal reconstruction and more blade end timing sensors, has a simple identification system, is quick and stable in operation, is simple and feasible, and can extract the natural frequency of the rotating blade by using the single-blade end timing sensor.
The above description is only a preferred embodiment of the present invention, and should not be taken as limiting the invention, and any modifications, equivalents, improvements, etc. made within the spirit and principle of the present invention should be included in the scope of the present invention.

Claims (8)

1. A method for extracting the natural frequency of a variable working condition rotating blade of a single-blade-end timing sensor is characterized by comprising the following steps of:
the method comprises the steps that firstly, a single-blade end timing sensor is used for obtaining time pulse of a rotating blade, the rotating speed n of the rotating blade is generated based on the time pulse, and the difference delta t between actual reaching time and theoretical reaching time is converted into displacement data according to the blade radius R and the rotating speed n of the rotating blade;
secondly, obtaining a sampling frequency-aliasing frequency graph with consistent aliasing frequency resolution based on the displacement data by using a variable window length short-time Fourier transform or least square estimation isochronous frequency analysis method;
thirdly, extracting characteristics of a sampling frequency-aliasing frequency diagram through Hough transformation or Radon transformation, wherein the characteristics comprise a straight slope and an intercept;
a fourth step of rounding the slope of the straight line to obtain a rounding result, and comparing the rounding result with the slope of the straight line to calculate the reliability;
and fifthly, carrying out weighted average on intercepts of all straight lines in the sampling frequency-aliasing frequency diagram according to the credibility to obtain an estimated value of the natural frequency.
2. The method for extracting the natural frequency of the variable working condition rotating blade of the single-blade-end timing sensor according to claim 1, wherein preferably, in the first step, the single-blade-end timing sensor is used for collecting the time pulse t of the rotating blade under the condition of variable rotating speed, the rotating speed is calculated by using the two time pulse of the same rotating blade,
Figure FDA0003240134760000011
where n (p) denotes the average rotational speed of the p-th turn in revolutions per minute,
Figure FDA0003240134760000012
indicating the time at which the ith vane reaches the sensor at circle p-1,
Figure FDA0003240134760000013
which represents the time, in seconds, at which the ith vane reaches the sensor at circle p +1,
the ideal arrival time is the time at which the blade reaches the sensor without vibration
Figure FDA0003240134760000014
Figure FDA0003240134760000015
Wherein
Figure FDA0003240134760000016
Represents the ideal time, θ, for the ith blade to reach the sensor at the p-th turniRepresenting the angle of the ith blade, alpha representing the installation angle of the sensor, and the displacement data is
Figure FDA0003240134760000021
Wherein
Figure FDA0003240134760000022
Denotes the ith blade at
Figure FDA0003240134760000023
The displacement of the moment.
3. The method for extracting the natural frequency of the variable working condition rotating blade of the single-blade-end timing sensor as claimed in claim 1, wherein in the second step, a sampling frequency step length Δ f is set during the short-time Fourier transform of the variable window lengthsAnd generating a sampling frequency sequence according to the rotating speed to determine the position center position of the short-time Fourier window:
Figure FDA0003240134760000024
wherein
Figure FDA0003240134760000025
Representing the lower bound of the selected analyzed speed range, a being an integer and representing FsNumber of middle elements, i.e. sequence FsThe value of a satisfies:
Figure FDA0003240134760000026
an upper bound representing the selected analyzed speed range,
Figure FDA0003240134760000027
wherein f isrRepresenting the collected speed vector, h1，h2Is an upper and lower bound overrun prevention threshold;
setting alias frequency resolution Δ RfAnd calculating the window length of each short-time Fourier window according to the rotating speed:
Figure FDA0003240134760000028
wherein N isL(m) denotes the window length of the mth window, i.e. the length of the data participating in the Fourier transform, Fs(m) denotes the m-th sequence of sampling frequencies, i.e. the sampling frequency of the m-th window position [. ]]oddRepresenting an operation taking an odd number of data nearby,
and calculating the data index which is actually closest to the sampling frequency according to the sampling frequency of the ideal window center:
Figure FDA0003240134760000029
wherein
Figure FDA00032401347600000210
Denotes the index value, f, for finding the minimum value of the post equationrIs the acquired frequency conversion data, and each circle can obtain a frequency conversion frIs a frequency vector, fr(index) represents frThe value of the middle-th index element,
taking the data index iindex as an intercepting data center and the window length NL(m) as data length, intercepting the displacement data y [ index- (N)L(m)-1)/2：index+(NL(m)-1)/2]Performing fast Fourier transform to represent the index- (N) of the displacement data yL(m) -1)/2 to index + (N)L(m) -1)/2 element values,
Figure FDA0003240134760000031
where y (n) is the sampled signal, i is an imaginary symbol,
Figure FDA0003240134760000032
n is the length of the acquired signal, the number of elements in y, N is an iteration number, from index- (N)L(m) -1)/2 traversal to index + (N)L(m) -1)/2, i.e., all elements in pass y, k is an integer from 0 to N-1, Y (k) represents the kth data after discrete Fourier transform,
setting alias frequency resolution Δ RfGenerating an aliased frequency sequence Fh：
Fh＝[0，ΔRf，2ΔRf，…，(b-1)ΔRf]Generating an amplitude matrix Aa×bWherein a is the length of the aliasing frequency sequence, b is the length of the sampling frequency sequence, the value of a is described above, b is an integer, and the value satisfies:
Figure FDA0003240134760000033
storing the absolute value of the Fourier transform result of the data in the mth window into an amplitude matrix Aa×bIn the m-th column in (1), all windows are traversed by the same analogy,
according to a sequence of sampling frequencies FsAlias frequency sequence FhAnd amplitude matrix Aa×bA sampling frequency-aliasing frequency graph is plotted, and round (·) represents a rounding operation.
4. The method for extracting the natural frequency of the variable-operating-condition rotating blade of the single-blade-end timing sensor according to claim 1, wherein in the second step,
based on aliasing frequency resolution Δ RfAnd a sampling frequency step Δ fsTo obtain
Fn＝[0，ΔRf，2ΔRf，…，(b-1)ΔRf]，
Figure FDA0003240134760000041
Wherein
Figure FDA0003240134760000042
Respectively representing the lower and upper bounds of the selected analyzed speed range, round (-) representing rounding,
calculating a window length sequence:
Figure FDA0003240134760000043
wherein represents NL(m) the window length of the mth window, i.e. the length of data participating in the Fourier transform, Fs(m) denotes the m-th sequence of sampling frequencies, i.e. the sampling frequency of the m-th window position [. ]]oddRepresenting an operation taking an odd number of data nearby,
calculating the data index actually closest to the sampling frequency based on the sampling frequency of the ideal window center:
Figure FDA0003240134760000044
wherein
Figure FDA0003240134760000045
The index value of the post formula to the minimum value is obtained, the data index is taken as a data interception center, and N is usedL(m) as data length, intercepting the displacement data y [ index- (N)L(m)-1)/2：index+(NL(m)-1)/2]Performing least square estimation to obtain amplitude coefficient by the following formula
Figure FDA0003240134760000046
Figure FDA0003240134760000047
Wherein QkIs a two-dimensional matrix composed of sine sequences and cosine sequences, the number of columns is 2,
Figure FDA0003240134760000048
is a two-dimensional matrix with 2 columns, and two values of each row are squared and then rooted to obtain an amplitude estimate AkY is the blade displacement, which is expressed as follows:
Figure FDA0003240134760000049
Figure FDA00032401347600000410
Qk＝[ck sk]，
y＝[y(index-(NL(m)-1)/2)，y(index-(NL(m)-1)/2+1)，…，y(index+(NL(m)-1)/2)]，
Figure FDA0003240134760000051
taking the value of k from 1 to a to obtain Am＝[A1，A2，…，Aa]The amplitude result A of least square estimation of the data in the mth windowmFilling into the two-dimensional matrix Aa×bWhen all windows are operated as above, a complete two-dimensional matrix A is obtaineda×bAccording to Fs，Fn，Aa×bPlotting a sampling frequency-aliased frequency map, wherein FsFor sampling a sequence of frequencies, FhFor aliasing of frequency sequences, Aa×bIs a two-dimensional amplitude matrix.
5. The method for extracting the natural frequency of the variable working condition rotating blade of the blade end timing sensor according to claim 1, wherein in the third step, an angle step Δ θ and a distance step Δ L of Hough transformation or Radon transformation are set to generate an angle sequence β and a distance step sequence L:
β＝[-90°，-90°+Δθ，-90°+2Δθ，…，90°]，
Figure FDA0003240134760000052
Figure FDA0003240134760000053
wherein H, W are the width and height pixel sizes of the image, respectively, where LRDistance step sequence, L, representing Radon transformHDistance step length sequence representing Hough transformation, angle sequence beta and distance generated by the distance step length sequenceAnd traversing the whole sampling frequency-aliasing frequency graph by the step length sequence L to realize feature extraction.
6. The method for extracting the natural frequency of the variable-operating-condition rotating blade of the blade-end timing sensor according to claim 1, wherein in the third step,
the method comprises the following steps of (1) expressing a straight line in a sampling frequency-aliasing frequency graph as a peak value in a new space after Radon transformation or Hough transformation, extracting a peak value coordinate (beta, L), and obtaining a slope and an intercept based on the peak value coordinate (beta, L), wherein the slope and the intercept of the graph after Hough transformation are calculated by a formula:
Figure FDA0003240134760000054
Figure FDA0003240134760000055
slope and intercept calculation formula of graph after Radon transformation:
Figure FDA0003240134760000061
Figure FDA0003240134760000062
where β is the corresponding angular coordinate, L is the corresponding distance coordinate, round (.) represents a rounding operation, where H, W represents the width, height pixel size of the image, k represents the slope, c represents the intercept, a, b represent the sampling frequency sequence F, respectivelysAnd an aliased frequency sequence FhLength of (1), Fs(a) Representing a sampling frequency sequence FsThe last element in (1), Fh(b) Representing an alias-taking frequency sequence FhThe last element in (1), Fs(l) Representing a sampling frequency sequence FsThe first element in (1), beta, L are respectively peak bright points in Hough spaceAbscissa and ordinate.
7. The method for extracting the natural frequency of the variable-operating-condition rotating blade of the blade-end timing sensor according to claim 1, wherein in the fourth step,
the weight function for confidence is:
Figure FDA0003240134760000063
wherein wkA weight value representing a k-th line; k is a radical ofkRepresents the slope of the k-th line and q is the total number of lines in the sampling frequency-alias frequency diagram.
8. The method for extracting the natural frequency of the variable-duty rotating blade of the blade tip timing sensor according to claim 7, wherein in the fifth step, the intercept estimation results of all straight lines in the graph are weighted and averaged according to confidence weight:
Figure FDA0003240134760000064
wherein c isiRepresents the intercept of the ith line,
Figure FDA0003240134760000065
representing the natural frequency estimate.
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