CN114091200A - Method for reducing rotating machinery bearing dynamic load recognition model ill-condition - Google Patents

Method for reducing rotating machinery bearing dynamic load recognition model ill-condition Download PDF

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CN114091200A
CN114091200A CN202111390635.3A CN202111390635A CN114091200A CN 114091200 A CN114091200 A CN 114091200A CN 202111390635 A CN202111390635 A CN 202111390635A CN 114091200 A CN114091200 A CN 114091200A
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刘志强
杨建刚
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Southeast University
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Abstract

The invention relates to a method for reducing the ill-condition of a rotating machinery bearing dynamic load recognition model, which is characterized in that the condition number-based response point measurement optimization is performed, all measurement point combination species are traversed, the condition number is calculated, and the optimal combination with the minimum condition number is selected to reduce the ill-condition caused by the linear correlation of the response point; under the condition of optimal combination, a frequency response function matrix of the bearing support system is extracted, a truncated singular value decomposition regularization method is adopted to decompose the frequency response function matrix, smaller singular values in the matrix are removed, a good state matrix is obtained to approach an original matrix, the influence of the too small singular values and corresponding eigenvectors on the solution is eliminated, the ill-conditioned characteristic of the equation is weakened, and the precision and the stability of the dynamic load identification result of the bearing are improved.

Description

Method for reducing rotating machinery bearing dynamic load recognition model ill-condition
Technical Field
The invention relates to the technical field of bearing dynamic load identification methods, in particular to a method for reducing the ill-condition of a rotary mechanical bearing dynamic load identification model.
Background
The dynamic load is an important factor influencing the safe and stable operation of the rotary machine, and the dynamic load identification technology is initially researched in the last 70 th century and mainly comprises a time domain identification method and a frequency domain identification method. The time domain identification method has high sensitivity to initial values, convolution operation is required, and the requirement on calculated amount is high; the frequency domain identification method forms a mature theoretical system and is the most common method for identifying the dynamic load. The frequency domain identification method comprises a frequency response function direct inversion method and a modal coordinate transformation method, the modal coordinate transformation method has higher requirement on the accuracy of modal parameters, and the frequency response function direct inversion method is simple and convenient and has wide application.
In the problem of identifying the dynamic load of a bearing of a rotating machine, the ill-conditioned problem of a frequency response matrix existing in the dynamic load is identified by utilizing a frequency response function direct inversion method, so that the solution is not qualified. Regularization technology was developed in the last 80 th century to improve the ill-posed nature of the dynamic load identification problem, including the gihonov regularization method (Tikhonov regularization method) and the truncated singular value decomposition (TSVD regularization method), and when regularization is used alone to improve matrix ill-posed nature, the problems exist: when small singular values are eliminated, effective measuring point response signals are easily removed by mistake, and the dynamic load identification precision is reduced.
Disclosure of Invention
Aiming at the defects of the prior art, the invention provides a method for reducing the ill-posed property of a dynamic load identification model of a rotary mechanical bearing, aiming at reducing the ill-posed property of a frequency response function in the dynamic load identification model of the rotary mechanical bearing, eliminating response points which are easy to cause the ill-posed property of the frequency response function and reducing the dynamic load identification error caused by a response error.
The technical scheme adopted by the invention is as follows:
a method for reducing the ill-posed characteristic of a rotary mechanical bearing dynamic load identification model comprises the following steps:
the method comprises the following steps: setting n bearings excited by the dynamic load at the same time, setting m response measuring points, and acquiring a bearing dynamic load excitation array and a corresponding response array;
step two: establishing a relationship between dynamic load and vibration response:
F＝(HHH)-1HHX
in the above formula, F is a dynamic load; h is a frequency response function matrix of all the response measuring points, HHA complex conjugate transpose matrix for H; x is a vibration response;
step three: fromRandomly selecting m from m response measuring pointsrN is less than or equal to mrM or less, the number of combinations of the response measuring points is
Figure BDA0003368668070000011
Calculating a system frequency response function matrix corresponding to the ith combination
Figure BDA0003368668070000012
Condition number of (1):
Figure BDA0003368668070000013
in the above formula, | | · | | is a matrix norm induced by the vector norm,
Figure BDA0003368668070000014
a Mole-Pennogos generalized pseudo-inverse matrix of the matrix H;
traversing all the measuring point combinations under the number of the response measuring points, calculating the condition number of the frequency response function matrix corresponding to each combination, finding out the matrix with the minimum condition number, and taking the corresponding measuring point combination as the optimal measuring point combination;
step four: and eliminating smaller singular values by using a truncated singular value decomposition method according to the vibration response and frequency response function matrix corresponding to the optimal measuring point combination, and calculating the dynamic load of the bearing.
The further technical scheme is as follows:
the fourth step specifically comprises:
1) obtaining a frequency response function matrix H corresponding to the optimal combination measuring point from the frequency response function matrixes H of all the response measuring pointsopAnd to HopIt performs singular value decomposition:
Figure BDA0003368668070000021
in the above formula, VnnAnd UmnIs a column vector orthogonal matrix, is a matrix HopDecomposed two unitary matrices, Umn＝{u1,u2,…,un}、Vnn＝{v1,v2,…,vn}; diagonal matrix sigmannHas a diagonal element of { σi}，i＝1,2,…,n，σi≧ 0 is the matrix HopAll singular values arranged in descending order;
2) obtaining the dynamic load to be identified by using the frequency response function matrix after singular value decomposition, wherein the calculation expression is as follows:
Figure BDA0003368668070000022
in the above formula, F is the dynamic load,
Figure BDA0003368668070000027
is a matrix HopMorel-pennoss generalized pseudo-inverse matrix of, XopExtracting the vibration response of the optimal combined measuring point from the vibration responses X of all the response measuring points;
3) identifying the dynamic load to be identified by adopting a truncation singular value decomposition normalization method to obtain an identified dynamic load regularization solution:
Figure BDA0003368668070000023
in the above formula, HkTo approximate the original matrix HopThe low-rank frequency response function matrix is provided, k is less than n;
Figure BDA0003368668070000024
in the above formula, sigmakThe method is characterized in that the diagonal matrix is obtained by filtering n-k minimum singular values in the diagonal matrix sigma.
The further technical scheme is as follows:
introducing the filtering factor into a dynamic load calculation expression to obtain an optimized dynamic load regularization solution:
Figure BDA0003368668070000025
wherein the filter factor is:
Figure BDA0003368668070000026
the invention has the following beneficial effects:
the method for optimizing the response measuring points adopts a combination mode of traversing all the response measuring point combinations and selecting the minimum condition number, so that not only are response points which are easy to cause the ill-condition of the frequency response function eliminated, but also the correlation among the response points is greatly reduced, and the ill-condition characteristic of the frequency response function matrix is further reduced;
on the basis of measuring point optimization based on condition numbers, a Truncated Singular Value Decomposition (TSVD) regularization method based on measuring point optimization is applied to elimination of matrix ill-condition problems in bearing dynamic load identification and elimination of ill-condition characteristics of a frequency response function matrix, so that dynamic load identification errors caused by response errors are reduced.
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FIG. 1 is a flow chart of a method of an embodiment of the present invention.
Fig. 2 is a schematic structural diagram of a test system according to an embodiment of the present invention.
FIG. 3 is a diagram of a stress analysis of the test system according to an embodiment of the present invention.
Detailed Description
The following describes embodiments of the present invention with reference to the drawings.
A method for reducing the ill-posed characteristic of a rotary mechanical bearing dynamic load identification model comprises the following steps:
the method comprises the following steps: setting n bearings excited by the dynamic load at the same time, setting m response measuring points, and acquiring a bearing dynamic load excitation array and a corresponding response array;
step two: establishing a relationship between dynamic load and vibration response:
F＝(HHH)-1HHX
in the above formula, F is the dynamic loadLoading; h is a frequency response function matrix of all response measuring points, and H belongs to Rm×nR is a real number field, HHA complex conjugate transpose matrix for H; x is the vibration response;
step three: randomly selecting m from m response measuring pointsrN is less than or equal to mrM or less, the number of combinations of the response measuring points is
Figure BDA0003368668070000035
Calculating a system frequency response function matrix corresponding to the ith combination
Figure BDA0003368668070000036
Condition number of (2):
Figure BDA0003368668070000034
in the above formula, | | · | | is a matrix norm induced by the vector norm,
Figure BDA0003368668070000037
a Mole-Pennogos generalized pseudo-inverse matrix of the matrix H;
traversing all the measuring point combinations under the number of the response measuring points, calculating the condition number of the frequency response function matrix corresponding to each combination, finding out the matrix with the minimum condition number, and taking the corresponding measuring point combination as the optimal measuring point combination;
step four: according to the vibration response and the frequency response function matrix corresponding to the optimal measuring point combination, a truncated singular value decomposition method is used for eliminating smaller singular values, and the dynamic load of the bearing is calculated; the method specifically comprises the following steps:
1) obtaining a frequency response function matrix H corresponding to the optimal combination measuring point from the frequency response function matrixes H of all the response measuring pointsopAnd to HopIt performs singular value decomposition:
Figure BDA0003368668070000031
in the above formula, VnnAnd UmnIs a column vector orthogonal matrix, is a matrixHopTwo decomposed unitary matrices respectively including a matrix HopLeft and right singular vectors of the singular values of (a); wherein, Umn＝{u1,u2,…,un}，Vnn＝{v1,v2,…,vn}; diagonal matrix sigmannHas a diagonal element of { σi}，i＝1,2,…,n，σi≧ 0 is the matrix HopAll singular values arranged in descending order.
2) Obtaining the dynamic load to be identified by using the frequency response function matrix after singular value decomposition, wherein the calculation expression is as follows:
Figure BDA0003368668070000032
in the above formula, F is the dynamic load,
Figure BDA0003368668070000033
is a matrix HopMorel-pennoss generalized pseudo-inverse matrix of, XopThe vibration response of the measuring points is extracted from the vibration responses X of all the responding measuring points and is optimally combined.
3) Identifying the dynamic load to be identified by adopting a truncated singular value decomposition regularization method to obtain an identified dynamic load regularization solution:
Figure BDA0003368668070000041
in the above formula, HkTo approximate the original matrix HopThe low-rank frequency response function matrix aims to eliminate the influence of undersize singular values and corresponding eigenvectors on normal solution, so that the ill-conditioned characteristic of the equation is weakened, and k is less than n;
expression of the regularization matrix:
Figure BDA0003368668070000042
in the above formula, sigmakIs to sum up n in the diagonal matrix sigma-k diagonal matrices obtained after filtering of the smallest singular values. Wherein k is a truncation number, and when k is reasonable in value, the matrix HkIs moderate, so that the dynamic load regularization solution FkIs more stable
Further, a filter factor f is introducedi：
Figure BDA0003368668070000043
Filter factor fiSubstituting into the dynamic load formula, the dynamic load regularization solution FkThe optimization is as follows:
Figure BDA0003368668070000044
the technical solution of the present application is further described below with specific examples.
Example 1
For the casing support system shown in fig. 2, the dynamic loads of the three bearings are identified, as shown in fig. 1, including the following steps:
(1) as shown in fig. 2, the rotor is removed, vibration sensor measuring points (X1, X2, X3, X4, X5, X6, X7, X8, X9, X10) are arranged on a plurality of sections of the casing, the vibration sensor measuring points (B1, B2, B3) are arranged on internal bearings, and the casing and the bearings are connected in a cone shell-web connection.
Respectively applying impact excitation to 10 measuring points on the surface of the casing to obtain vibration responses of 3 bearings, and obtaining a 10 multiplied by 3 dimensional frequency response function matrix H from the bearings to the surface of the casing by utilizing the reciprocity of the frequency response function, wherein the coherence coefficient is more than 0.7, and the frequency response function is considered to be reliable.
(2) Installing a rotor part, as shown in FIG. 3, which is a stress analysis diagram of the rotor, wherein F1-F3 are dynamic loads borne by 3 bearings; u1 and U2 are unbalanced forces borne by the two wheels; l1-l4 are the distances between the bearings and the wheel disc. Unbalance amounts are arranged on two wheel discs of the rotor, unbalance forces (U1, U2) caused by the unbalance amounts simulate different dynamic load working conditions, and vibration responses X of all measuring points on the surface of the casing in an operating state are measured by a sensor.
(3) Optimizing the measuring points, wherein the number of the measuring points is not less than the number of the dynamic loads to be identified, namely the number of the selected measuring points is at least 3, and at least 3 measuring points are selected from 10 measuring points, so that the total number is
Figure BDA0003368668070000045
And (4) a combination mode is adopted, the condition number of the lower support system frequency response function matrix of each combination mode is calculated, and the measuring point combination with the minimum condition number is the optimized measuring point combination.
Obtaining an optimized measuring point frequency response function matrix H from a 10 multiplied by 3 dimensional measuring point frequency response function matrix Hop(ii) a Extracting optimized measuring point combined response X from all measuring point responses Xop。
(4) Eliminating and optimizing measuring point frequency response function matrix H by using Truncated Singular Value Decomposition (TSVD) regularization methodopThe influence of medium and small singular values and the characteristic vectors thereof on the solution weakens the ill-condition characteristics of the matrix to obtain a good condition frequency response function matrix Hk-op of the optimized measuring point, and X is used for calculating the value of the medium and small singular values and the influence of the characteristic vectors thereof on the solutionopAnd HkSubstituting into the dynamic load calculation formula to obtain
Figure BDA0003368668070000046
Thus, 3 dynamic bearing loads (F1, F2, F3) were obtained.
(5) 3 bearing dynamic loads under arbitrary two kinds of operating modes are discerned, according to power and moment balance principle, calculate the unbalance force that the dynamic load that the bearing receives is equivalent to on two rim plates:
Figure BDA0003368668070000051
Figure BDA0003368668070000052
in the formula of U1、U2Unbalanced forces borne by the two wheel discs respectively; f1、F2、F3The dynamic loads borne by the 3 bearings respectively; l1、l2、l3、l4Are respectively eachThe distance between the bearing and the wheel disc.
(6) And comparing the wheel disc unbalanced force vector difference calculated under the two working conditions with the actual unbalanced force vector difference, and verifying the dynamic load identification precision. The result shows that the amplitude error of the bearing dynamic load identification is not more than 20%, and the phase error is about 15 degrees.
Comparative example 1
The method is the same as the test device and conditions adopted in the embodiment 1, and has the difference that the adopted identification method does not optimize the surface measuring points of the casing, only inverts the frequency response function H of the lower support system of all measuring points of the casing, and weakens the matrix ill-condition by utilizing a Truncated Singular Value Decomposition (TSVD) normalization method so as to realize the identification of the dynamic load of the bearing, and comprises the following steps:
(1) after the rotor part is removed, impact excitation is respectively applied to 10 measuring points on the surface of the casing to obtain vibration responses of 3 bearings, and a 10 multiplied by 3 dimensional frequency response function matrix H from the bearings to the surface of the casing is obtained by utilizing the reciprocity of the frequency response function. The rotor part is installed, and the vibration response X of 10 measuring points on the surface of the casing is measured by a sensor.
(2) Performing singular value decomposition on the frequency response function matrix H by using a Truncated Singular Value Decomposition (TSVD) regularization method, and eliminating smaller singular values to obtain a good state frequency response function matrix Hk。
(3) Selecting any two dynamic load working conditions, and combining X and HkSubstituting into the dynamic load calculation formula to obtain
Figure BDA0003368668070000053
Thus identifying 3 bearing dynamic loads without point optimization. According to the force and moment balance principle, the dynamic load of the three bearings is equivalent to the unbalanced force on the two wheel discs.
(4) And comparing the calculated wheel disc unbalanced force vector difference under the two working conditions with the actual unbalanced force vector difference, and verifying the dynamic load identification precision. The result shows that the bearing dynamic load identification amplitude error is about 28%, and the phase error is about 20 degrees.
Comparative example 2
The method is the same as the test device and conditions adopted in the embodiment 1, and has the difference that the adopted identification method only optimizes the surface measuring point of the casing, and does not utilize a Truncated Singular Value Decomposition (TSVD) regularization method to process the frequency response function of the support system so as to realize the identification of the dynamic load of the bearing, and the method comprises the following steps:
(1) after the rotor part is removed, impact excitation is respectively applied to 10 measuring points on the surface of the casing to obtain vibration responses of 3 bearings, and a 10 multiplied by 3 dimensional frequency response function matrix H from the bearings to the surface of the casing is obtained by utilizing the reciprocity of the frequency response function. The rotor part is installed, and the vibration response X of 10 measuring points on the surface of the casing is measured by a sensor.
(2) And optimizing the measuring points, traversing all measuring point combinations, and respectively calculating the condition number of the corresponding frequency response function matrix under each combination, wherein the measuring point combination with the minimum condition number is the optimized measuring point combination.
Extracting the vibration response X of the optimized measuring point combination from the vibration responses of the 10 measuring pointsopExtracting an optimized measuring point frequency response function matrix H from a 10 multiplied by 3 dimensional frequency response function matrix Hop。
(3) Selecting any two dynamic load working conditions, and enabling X to be in a state of being parallel to the working conditionsopAnd HopSubstituting into the dynamic load calculation formula to obtain
Figure BDA0003368668070000054
Thus identifying 3 bearing dynamic loads through point optimization. And calculating the unbalanced force of the dynamic load of the three bearings equivalent to the two wheel discs according to the force and moment balance principle.
(4) And comparing the wheel disc unbalanced force vector difference calculated under the two working conditions with the actual unbalanced force vector difference, and verifying the dynamic load identification precision. The result shows that the error of the amplitude value of the bearing dynamic load identification is about 45 percent, and the error of the phase position is about 35 degrees.
According to the specific embodiment and the comparative example, the method for reducing the ill-conditioned of the rotary mechanical bearing dynamic load recognition model selects the optimized measuring point combination with the minimum condition number by traversing all measuring point combinations. The pathological characteristics caused by linear correlation among response points are eliminated, and effective response signals of the measuring points can be reserved; a TSVD regularization method is adopted, and on the basis of measuring point optimization, smaller singular values are removed, and the dynamic load identification precision is improved.

Claims (3)

1. A method for reducing the ill-posed characteristic of a rotary mechanical bearing dynamic load identification model is characterized by comprising the following steps:
the method comprises the following steps: setting n bearings excited by the dynamic load at the same time, setting m response measuring points, and acquiring a bearing dynamic load excitation array and a corresponding response array;
step two: establishing a relationship between dynamic load and vibration response:
F＝(HHH)-1HHX
in the above formula, F is a dynamic load; h is a frequency response function matrix of all the response measuring points, HHA complex conjugate transpose matrix for H; x is the vibration response;
step three: randomly selecting m from m response measuring pointsrN is less than or equal to mrM or less, the number of combinations of the response measuring points is
Figure FDA0003368668060000011
Calculating a system frequency response function matrix corresponding to the ith combination
Figure FDA0003368668060000012
Condition number of (2):
Figure FDA0003368668060000013
in the above formula, | | · | | is a matrix norm induced by the vector norm,
Figure FDA0003368668060000014
a Mole-Pennogos generalized pseudo-inverse matrix of the matrix H;
traversing all the measuring point combinations under the number of the response measuring points, calculating the condition number of the frequency response function matrix corresponding to each combination, finding out the matrix with the minimum condition number, and taking the corresponding measuring point combination as the optimal measuring point combination;
step four: and eliminating smaller singular values by using a truncated singular value decomposition method according to the vibration response and frequency response function matrix corresponding to the optimal measuring point combination, and calculating the dynamic load of the bearing.
2. The method for reducing the ill-posed nature of the rotating machinery bearing dynamic load identification model according to claim 1, wherein the fourth step specifically comprises:
1) obtaining a frequency response function matrix H corresponding to the optimal combination measuring point from the frequency response function matrixes H of all the response measuring pointsopAnd to HopIt performs singular value decomposition:
Figure FDA0003368668060000015
in the above formula, VnnAnd UmnIs a column vector orthogonal matrix, is a matrix HopDecomposed two unitary matrices, Umn＝{u1,u2,…,un}、Vnn＝{v1,v2,…,vn}; diagonal matrix sigmannHas a diagonal element of { σi}，i＝1,2,…,n，σi≧ 0 is the matrix HopAll singular values arranged in a descending order;
2) obtaining the dynamic load to be identified by using the frequency response function matrix after singular value decomposition, wherein the calculation expression is as follows:
Figure FDA0003368668060000016
in the above formula, F is the dynamic load,
Figure FDA0003368668060000017
is a matrix HopMorel-pennoss generalized pseudo-inverse matrix of, XopExtracting the vibration response of the optimal combined measuring point from the vibration responses X of all the response measuring points;
3) identifying the dynamic load to be identified by adopting a truncated singular value decomposition regularization method to obtain an identified dynamic load regularization solution:
Figure FDA0003368668060000021
in the above formula, HkTo approximate the original matrix HopThe low-rank frequency response function matrix is provided, k is less than n;
Figure FDA0003368668060000022
in the above formula, sigmakThe method is characterized in that the diagonal matrix is obtained by filtering n-k minimum singular values in the diagonal matrix sigma.
3. The method for reducing the ill-conditioned of a rotating mechanical bearing dynamic load identification model according to claim 2, wherein the filtering factor is introduced into a dynamic load calculation expression to obtain an optimized dynamic load regularization solution as:
Figure FDA0003368668060000023
wherein the filtering factor:
Figure FDA0003368668060000024
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WO2023246117A1 (en) * 2022-06-21 2023-12-28 山东大学 Load identification method and system based on hybrid iterative regularization
CN117473795A (en) * 2023-12-26 2024-01-30 烟台哈尔滨工程大学研究院 Distributed ice load identification mathematical model pathological elimination method
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Cited By (5)

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Publication number Priority date Publication date Assignee Title
WO2023246117A1 (en) * 2022-06-21 2023-12-28 山东大学 Load identification method and system based on hybrid iterative regularization
CN117473795A (en) * 2023-12-26 2024-01-30 烟台哈尔滨工程大学研究院 Distributed ice load identification mathematical model pathological elimination method
CN117473795B (en) * 2023-12-26 2024-04-19 烟台哈尔滨工程大学研究院 Distributed ice load identification mathematical model pathological elimination method
CN117494476A (en) * 2023-12-29 2024-02-02 烟台哈尔滨工程大学研究院 Measuring point optimization method for improving pneumatic load identification stability of fan tower
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