CN112629786A - Working mode parameter identification method and equipment fault diagnosis method - Google Patents
Working mode parameter identification method and equipment fault diagnosis method Download PDFInfo
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Abstract
The invention relates to a working modal parameter identification method and an equipment fault diagnosis method, and relates to the technical field of modal parameter identification. The working mode parameter identification method comprises the following steps: acquiring a time domain vibration response signal matrix formed by time domain vibration response signals detected by a vibration sensor within a preset time in a one-dimensional structure of a working modal parameter to be determined; obtaining a modal response matrix by utilizing a Laplace characteristic mapping method according to the time domain vibration response signal matrix; obtaining a modal shape matrix by utilizing a least square method generalized inverse method according to the modal response matrix; and obtaining the modal natural frequency by utilizing a single degree of freedom technology or a Fourier transform method according to the modal response matrix. The invention applies the Laplace feature mapping in manifold learning to the working mode analysis, and has lower time and space complexity.
Description
Technical Field
The invention relates to the technical field of modal parameter identification, in particular to a working modal parameter identification method and an equipment fault diagnosis method.
Background
The mode is the vibration characteristic of the structure, and parameters (such as mode natural frequency, vibration mode, damping ratio and the like) of each order of mode are identified through an experimental mode analysis method, so that the dynamic characteristic of the structure can be known, and further damage identification of the structure, fault detection of equipment and the like are performed. However, for many large complex structures, the only excitation available is ambient excitation in the operating state, which results in an inability to measure excitation input. To solve this problem, a method of identifying the modal parameters of a structure by using only the output response of the structure is proposed and widely used.
Currently, there are various methods for identifying the modal parameters of the structure by using the output response of the structure, for example, the modal parameters are identified by using principal component analysis, so that the problem of false modal in the identification process of other methods is solved. The principal component analysis method is a linear method for reducing dimensions by converting a plurality of variables into a few comprehensive variables, namely principal components, through the research on the internal structure of a correlation matrix or a covariance matrix of original data. However, the principal component analysis method must calculate all principal components, which results in high time complexity of the modal parameter identification method using principal component analysis.
Disclosure of Invention
The invention aims to provide a working modal parameter identification method and an equipment fault diagnosis method, and aims to solve the problem that the existing modal parameter identification method is high in time complexity.
In order to achieve the purpose, the invention provides the following scheme:
a working mode parameter identification method comprises the following steps:
arranging a plurality of vibration sensors in a one-dimensional structure of which working modal parameters are to be determined; the vibration sensor is used for detecting a time domain vibration response signal of the linear time-invariant system under the excitation of a natural environment within a preset time; the working modal parameters comprise a modal shape and a modal natural frequency;
acquiring a time domain vibration response signal matrix formed by the time domain vibration response signals detected by each vibration sensor within preset time;
obtaining a modal response matrix by utilizing a Laplace characteristic mapping method according to the time domain vibration response signal matrix;
obtaining a modal shape matrix by utilizing a least square method generalized inverse method according to the modal response matrix;
and obtaining the modal natural frequency by utilizing a single degree of freedom technology or a Fourier transform method according to the modal response matrix.
Optionally, the obtaining a modal response matrix by using a laplacian feature mapping method according to the time domain vibration response signal matrix specifically includes:
the time domain vibration response signal matrix is
Wherein
Representing a time domain vibration response signal detected by a jth vibration sensor within a preset time t, wherein n represents the total number of the vibration sensors;
acquiring K adjacent time domain vibration response signals closest to the jth time domain vibration response signal;
reconstructing local structural features of the time domain vibration response signal matrix by using the weights of all the adjacent time domain vibration response signals;
performing eigenvalue decomposition on the local structural characteristics of the time domain vibration response signal matrix by using a Laplace eigenvalue mapping method to obtain d eigenvectors corresponding to the minimum non-zero eigenvalues;
and the eigenvectors corresponding to the d minimum non-zero eigenvalues form a time domain vibration response signal dimension reduction matrix, and the modal response matrix corresponds to the time domain vibration response signal dimension reduction matrix.
Optionally, the reconstructing the local structural feature of the time domain vibration response signal matrix by using the weights of all the adjacent time domain vibration response signals specifically includes:
determining the weight of the jth time domain vibration response signal and the kth adjacent time domain vibration response signal through a Gaussian kernel function according to the jth time domain vibration response signal and the kth adjacent time domain vibration response signal which is closest to the jth time domain vibration response signal; k1, 2,. K;
all the time domain vibration response signals and the weights of the adjacent time domain vibration response signals corresponding to the time domain vibration response signals form an adjacency matrix;
according to the weight of the jth time domain vibration response signal and the kth adjacent time domain vibration response signal, the formula is adopted
Determining the degree of the time domain vibration response signal; the degree matrix is a diagonal matrix formed by the degrees of the time domain vibration response signals; wherein the content of the first and second substances,
in the formula, DjkRepresenting the degree, w, of the j-th of said time-domain vibration response signaljkRepresenting the weight of the jth time domain vibration response signal and the kth adjacent time domain vibration response signal, wherein sigma represents the width parameter of the Gaussian kernel function; the local structural characteristics of the time domain vibration response signal matrix comprise a degree matrix and a Laplace matrix;
determining a laplacian matrix by a formula L ═ D-W according to the adjacency matrix and the degree matrix; where L denotes a laplacian matrix, D denotes a degree matrix, and W denotes an adjacency matrix.
Optionally, the obtaining a modal shape matrix by using a least square method generalized inverse method according to the modal response matrix specifically includes:
according to the modal response matrix, utilizing a least square generalized inverse method phi ═ X (t) QT(t)(Q(t)QT(t))-1Solving to obtain a modal shape matrix; wherein Φ represents a mode shape matrix, x (t) represents a time domain vibration response signal matrix, and q (t) represents a mode response matrix.
Optionally, obtaining a modal natural frequency by using a fourier transform method according to the modal response matrix, specifically including:
substituting the modal response matrix into a Fourier transform formula
Obtaining frequency domain data; the maximum frequency value in the frequency domain data is the modal natural frequency.
A working mode parameter identification method comprises the following steps:
arranging a plurality of vibration sensors in a three-dimensional structure of which working modal parameters are to be determined; the vibration sensor is used for detecting a time domain vibration response signal of the linear time-invariant system under the excitation of a natural environment within a preset time; the working modal parameters comprise a modal shape and a modal natural frequency;
acquiring a three-dimensional time domain vibration response signal matrix formed by the time domain vibration response signals detected by each vibration sensor within preset time;
discretizing the three-dimensional time domain vibration response signal matrix to obtain a vibration response signal matrix in the X direction, a vibration response signal matrix in the Y direction and a vibration response signal matrix in the Z direction; x, Y and Z are coordinate axes of a space rectangular coordinate system;
forming an integral modal response matrix of the three-dimensional structure by the vibration response signal matrix in the X direction, the vibration response signal matrix in the Y direction and the vibration response signal matrix in the Z direction;
obtaining a modal coordinate response matrix by utilizing a Laplace characteristic mapping method according to the overall modal response matrix;
obtaining a modal shape matrix by utilizing a least square method generalized inverse method according to the modal coordinate response matrix;
and obtaining the modal natural frequency by utilizing a single degree of freedom technology or a Fourier transform method according to the modal coordinate response matrix.
Optionally, the obtaining a modal coordinate response matrix by using a laplacian feature mapping method according to the overall modal response matrix specifically includes:
the overall modal response matrix is
Wherein (X)Three)H×T(t) represents a vibration response signal matrix in the X direction, (Y)Three)H×T(t) a vibration response signal matrix in the Y direction, (Z)Three)H×T(t) a matrix of vibration response signals representing the Z direction;
obtaining the K nearest to each X-direction time domain vibration response signal in the vibration response signal matrix in the X directionXAdjacent X-direction time domain vibration response signals, and K nearest to each Y-direction time domain vibration response signal in the vibration response signal matrix in the Y directionYAdjacent time domain vibration response signals in Y direction and K nearest to each time domain vibration response signal in Z direction in vibration response signal matrix in Z directionZTime domain vibration response signals in adjacent Z directions;
reconstructing the X-direction local structural feature of the X-direction time domain vibration response signal matrix by using the weights of all the adjacent X-direction time domain vibration response signals;
reconstructing Y-direction local structural features of the Y-direction time domain vibration response signal matrix by using the weights of all the adjacent Y-direction time domain vibration response signals;
reconstructing Z-direction local structural features of the Z-direction time domain vibration response signal matrix by using the weights of all the adjacent Z-direction time domain vibration response signals;
respectively aligning the images by using a Laplace characteristic mapping methodCarrying out characteristic value decomposition on the X-direction local structural feature, the Y-direction local structural feature and the Z-direction local structural feature to obtain dXThe X-direction characteristic vector, d, corresponding to the minimum non-zero eigenvalue of the X-direction local structural characteristic decompositionYY-direction feature vector d corresponding to minimum non-zero eigenvalue of Y-direction local structural feature decompositionZZ-direction feature vectors corresponding to the minimum non-zero eigenvalues of the Z-direction local structural feature decomposition;
dXforming an X-direction time domain vibration response signal dimension reduction matrix by the X-direction characteristic vectors, dYForming a Y-direction time domain vibration response signal dimension reduction matrix by the Y-direction characteristic vectors, dZForming a Z-direction time domain vibration response signal dimension reduction matrix by the Z-direction characteristic vectors; the modal response matrix in the X direction corresponds to the dimension reduction matrix of the time domain vibration response signal in the X direction, the modal response matrix in the Y direction corresponds to the dimension reduction matrix of the time domain vibration response signal in the Y direction, and the modal response matrix in the Z direction corresponds to the dimension reduction matrix of the time domain vibration response signal in the Z direction;
and forming a modal coordinate response matrix by the modal response matrix in the X direction, the modal response matrix in the Y direction and the modal response matrix in the Z direction.
Optionally, the reconstructing the X-direction local structural feature of the X-direction time domain vibration response signal matrix by using the weights of all the adjacent X-direction time domain vibration response signals specifically includes:
according to jXThe time domain vibration response signal in the X direction and the distance jXThe k-th nearest to the X-direction time domain vibration response signalXDetermining j th time domain vibration response signal in X direction through Gaussian kernel functionXThe time domain vibration response signal in the X direction and the kthXWeights of the adjacent X-direction time domain vibration response signals; k is a radical ofX＝1,2,...,KX；
All the X-direction time domain vibration response signals and the weights of the adjacent X-direction time domain vibration response signals corresponding to the X-direction time domain vibration response signals form an X-direction adjacency matrix;
according to jXThe time domain vibration response signal in the X direction and the kthXThe weight of the time domain vibration response signal in the adjacent X direction is calculated by formula
Determining an X-direction degree matrix; the X-direction degree matrix is composed of
A diagonal matrix is formed; wherein the content of the first and second substances,
denotes the j (th)XThe degree of the X-direction time-domain vibration response signal,
denotes the j (th)XThe time domain vibration response signal in the X direction and the kthXWeights of the adjacent X-direction time domain vibration response signals; the X-direction local structural characteristics of the X-direction time domain vibration response signal matrix comprise an X-direction degree matrix and an X-direction Laplace matrix;
according to the X-direction adjacency matrix and the X-direction degree matrix, a formula L is obtainedX＝DX-WXDetermining an X-direction Laplace matrix; wherein L isXDenotes the X-direction Laplace matrix, DXRepresenting the X-direction degree matrix, WXRepresenting an X-direction adjacency matrix.
Optionally, the obtaining a modal shape matrix by using a least square method generalized inverse method according to the modal coordinate response matrix specifically includes:
according to the modal coordinate response matrix, utilizing least square method generalized inverse method
Solving to obtain a modal shape matrix; wherein (phi)Three)3H×SRepresents a mode shape matrix, (H)Three)3H×T(t) represents a wholeModal response matrix, (Q)Three)S×T(t) represents a modal coordinate response matrix,
a transpose matrix representing a modal coordinate response matrix.
An equipment fault diagnosis method comprising:
if the equipment to be diagnosed is of a one-dimensional structure, determining the working modal parameters of the equipment to be diagnosed at the current moment by using the working modal parameter identification method;
if the equipment to be diagnosed is in a three-dimensional structure, determining the working modal parameters of the equipment to be diagnosed at the current moment by using the working modal parameter identification method;
obtaining working mode parameters of the equipment to be diagnosed at the last moment;
judging whether the determined working modal parameter of the equipment to be diagnosed at the current moment is completely consistent with the working modal parameter of the equipment to be diagnosed at the last moment or not to obtain a first judgment result;
if the first judgment result is yes, the equipment to be diagnosed has no fault;
and if the first judgment result is negative, the equipment to be diagnosed has a fault.
According to the specific embodiment provided by the invention, the invention discloses the following technical effects:
the invention provides a working mode parameter identification method and an equipment fault diagnosis method. The working mode parameter identification method comprises the following steps: arranging a plurality of vibration sensors in a one-dimensional structure of which working modal parameters are to be determined; the vibration sensor is used for detecting a time domain vibration response signal of the linear time-invariant system under the excitation of a natural environment within preset time; the working modal parameters comprise a modal shape and a modal natural frequency; acquiring a time domain vibration response signal matrix formed by time domain vibration response signals detected by each vibration sensor within preset time; obtaining a modal response matrix by utilizing a Laplace characteristic mapping method according to the time domain vibration response signal matrix; obtaining a modal shape matrix by utilizing a least square method generalized inverse method according to the modal response matrix; and obtaining the modal natural frequency by utilizing a single degree of freedom technology or a Fourier transform method according to the modal response matrix. According to the invention, Laplace feature mapping in manifold learning is applied to the working mode analysis, so that the time and space complexity is reduced, and the identification precision of working mode parameters is improved.
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In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings needed to be used in the embodiments will be briefly described below, and it is obvious that the drawings in the following description are only some embodiments of the present invention, and it is obvious for those skilled in the art to obtain other drawings without inventive exercise.
Fig. 1 is a flowchart of a method for identifying working mode parameters of a one-dimensional structure according to an embodiment of the present invention;
fig. 2 is a flowchart of a method for identifying working mode parameters of a three-dimensional structure according to an embodiment of the present invention;
FIG. 3 is a flow chart of a method for diagnosing equipment failure according to an embodiment of the present invention;
FIG. 4 is a finite element model of a three-dimensional cylindrical shell provided by an embodiment of the present invention;
FIG. 5 is a modal natural frequency plot of a three-dimensional cylindrical shell provided by an embodiment of the present invention;
FIG. 6 illustrates a mode shape of a three-dimensional cylindrical shell according to an embodiment of the present invention; FIG. 6(a) is the true mode shape of a three-dimensional cylindrical shell at orders 1,2, 3, 4 and 7; fig. 6(b) shows the mode shapes of the three-dimensional cylindrical shell at 1 st, 2 nd, 3 rd, 4 th and 7 th orders determined by the working mode parameter identification method.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
The invention aims to provide a working modal parameter identification method and an equipment fault diagnosis method, and aims to solve the problem that the existing modal parameter identification method is high in time complexity.
In order to make the aforementioned objects, features and advantages of the present invention comprehensible, embodiments accompanied with figures are described in further detail below.
Manifold is a geometric concept that represents a low-dimensional geometry that is tessellated in a high-dimensional space. Based on the geometric concept, the data after dimension reduction needs to be kept in the dimension reduction process of manifold learning, and the geometric constraint relation related to the manifold in the high-dimensional space is also satisfied. At present, algorithms widely used in manifold learning include an equidistant mapping, a local linear embedding algorithm, a laplacian feature mapping method and the like. In recent years, manifold learning is widely applied in a plurality of engineering fields such as image processing, for example, a manifold learning method using local linear embedding is used to identify working mode parameters of a complex three-dimensional continuum structure. The invention aims to introduce a Laplace feature mapping method in manifold learning into a dynamic system to identify working mode parameters of a linear time-invariant structure.
The embodiment provides a working mode parameter identification method which is applied to a one-dimensional structure. Fig. 1 is a flowchart of a working mode parameter identification method for a one-dimensional structure according to an embodiment of the present invention, and referring to fig. 1, the working mode parameter identification method includes:
wherein the content of the first and second substances,
representing a time domain vibration response signal measured by a jth sensor within a preset time t; n denotes the total number of vibration sensors arranged on the one-dimensional structure, j ═ 1, 2.., n; t represents a preset time; t represents the total number of sampling points in the time domain within a preset time T, i is 1, 2. x is the number ofj(i) Representing the vibration response signal measured by the jth sensor at the ith sampling point; x is the number ofj(T) represents the vibration response signal measured by the jth sensor at the tth sampling point,
representing a matrix of dimension n x T.
And 103, obtaining a modal response matrix by utilizing a Laplace characteristic mapping method according to the time domain vibration response signal matrix.
Step 103 specifically comprises:
time domain vibration response signal matrix of
Wherein
Represents the time-domain vibration response signal detected by the jth vibration sensor within the preset time t, and n represents the total number of the vibration sensors.
And acquiring K adjacent time domain vibration response signals closest to the jth time domain vibration response signal. Obtaining a time domain vibration response signal matrix X (t) in the step 102, and regarding each point in the time domain vibration response signal matrix
Find K neighbors nearest to it, i.e. adjacent time domain vibration response signals
The method for calculating the distance between any two time-domain vibration response signals is a K-nearest neighbor algorithm.
And reconstructing local structural features of the time domain vibration response signal matrix by using the weights of all adjacent time domain vibration response signals. The method specifically comprises the following steps:
determining the weight of the jth time domain vibration response signal and the kth adjacent time domain vibration response signal through a Gaussian kernel function according to the jth time domain vibration response signal and the kth adjacent time domain vibration response signal which is closest to the jth time domain vibration response signal; k is 1, 2. Weight w of each neighborjkSize may be determined by a Gaussian kernel function
Calculation of wjkRepresenting the j time-domain vibration response signal
And adjacent time domain vibration response signal
The weight on the adjacency graph, σ, is the width parameter of the gaussian kernel.
All the time domain vibration response signals and the weights of the adjacent time domain vibration response signals corresponding to the time domain vibration response signals form an adjacency matrix. Through wjkConstructing a adjacency matrix W ═ Wjk]To reconstruct the local structural features of the time-domain vibration response signal matrix x (t).
According to the weight of the jth time domain vibration response signal and the kth adjacent time domain vibration response signal, the formula is used
Determining time-domain vibrationsThe degree of the response signal; the degree matrix is a diagonal matrix formed by the degrees of the time domain vibration response signals; wherein D isjkDegree, w, of a j-th time-domain vibration response signaljkRepresenting the weight of the jth time domain vibration response signal and the kth adjacent time domain vibration response signal; the local structural features of the time domain vibration response signal matrix include a degree matrix and a laplacian matrix. Let diagonal matrix D be the degree matrix of x (t) graph and L be the laplacian matrix of the graph.
Determining a Laplace matrix according to the adjacency matrix and the degree matrix by using a formula L-D-W; where L denotes a laplacian matrix, D denotes a degree matrix, and W denotes an adjacency matrix.
And performing eigenvalue decomposition on the local structural characteristics of the time domain vibration response signal matrix by using a Laplace eigenvalue mapping method to obtain d eigenvectors corresponding to the minimum non-zero eigenvalues. Laplace eigenmap pass pair is a formula of Laplace eigenmap
(
Eigenvectors corresponding to eigenvalues λ) are subjected to eigenvalue decomposition and
decomposed d (d < n) minimum non-zero eigenvalues lambda1,λ2,…,λd',…,λdCorresponding feature vector
Outputting the result after dimension reduction to obtain a matrix after dimension reduction, namely a time domain vibration response signal dimension reduction matrix
The purpose of dimension reduction can be achieved, Y (t) corresponds to the modal response matrix Q (t).
Denotes λd'Represents the d 'th minimum non-zero characteristic value, d' 1, 2.., d;
representing the eigenvector corresponding to the d' th minimum non-zero eigenvalue, wherein the value of d is the same as the order of modal identification, and generally d is<1/10n is considered to be d much smaller than n.
And d eigenvectors corresponding to the minimum non-zero eigenvalues form a time domain vibration response signal dimension reduction matrix, and the modal response matrix corresponds to the time domain vibration response signal dimension reduction matrix.
And 104, obtaining a modal shape matrix by using a least square method generalized inverse method according to the modal response matrix.
Step 104 specifically includes:
according to the modal response matrix, using a least square generalized inverse method phi ═ X (t) QT(t)(Q(t)QT(t))-1Solving to obtain a modal shape matrix; wherein Φ represents a mode shape matrix, x (t) represents a time domain vibration response signal matrix, and q (t) represents a mode response matrix. In the modal coordinate, the time-domain vibration response signal matrix x (t) may be decomposed into x (t) ═ Φ Q (t), where x (t) and Q (t) are known, and the modal shape matrix Φ is obtained by using the least square method generalized inverse method whose formula is Φ ═ x (t) Q (t)T(t)(Q(t)QT(t))-1。
And 105, obtaining the natural frequency of the mode by utilizing a single degree of freedom (SDOF) or a Fourier transform method according to the mode response matrix.
According to the modal response matrix, obtaining modal natural frequency by using a Fourier transform method, which specifically comprises the following steps:
substituting the modal response matrix into a Fourier transform formula
Obtaining frequency domain data; in the amplitude-frequency map in the frequency domain data, the frequency value corresponding to the maximum amplitude is the modal natural frequency.
In the embodiment, the accuracy of identifying the working modal parameters by the modal shape matrix phi is quantitatively evaluated by adopting the modal confidence parameters MAC, and the effectiveness of identifying the working modal parameters by an algorithm is measured. The modal confidence formula is specifically:
wherein phi isiIs the identified ith mode shape matrix,
represents the true ith mode shape matrix, phii TAnd
respectively represents phiiAnd
the transpose of (a) is performed,
represents the inner product of two vectors and represents the inner product of the two vectors,
is indicative of phiiAnd
to the extent of the similarity in the direction of the line,
the more its value is close to 1, the higher the accuracy of the mode shape matrix identification. The function of evaluating the accuracy of the modal shape matrix is that if the MAC value is closer to 1, the higher the identification accuracy of the modal shape matrix is, which indicates that the effectiveness of the working modal parameter identification method is higher.
The embodiment also provides a working mode parameter identification method which is applied to a three-dimensional structure. Fig. 2 is a flowchart of a method for identifying working mode parameters of a three-dimensional structure according to an embodiment of the present invention, and referring to fig. 2, the method for identifying working mode parameters includes:
wherein, XThree(t) represents a time-domain vibration response signal in the X direction, YThree(t) time-domain vibration response signal in Y-direction, ZThree(t) representing a time domain vibration response signal in the Z direction, X, Y, Z corresponding to coordinate axes in the X direction, the Y direction and the Z direction of the three-dimensional space rectangular coordinate system respectively; o denotes a modal shape matrix in the X direction, ρ denotes a modal shape matrix in the Y direction, and θ denotes a modal shape matrix in the Z direction (i.e., (Φ)Three)3H×S＝[ο；ρ；υ]) (ii) a A (t) represents the time domain vibration response signal of each order
A constructed modal response matrix; m represents the order of the mode, and the range value is 1 to infinity;
corresponding to X, Y, Z th order mode shape in three directions. The mode shape of the mth order mode of the complex three-dimensional structure can be assembled by assembling X, Y, Z into the mth order mode shape in three directions
And (4) performing representation.
Also represents the modal coordinates (in terms of m-th order mode of a complex three-dimensional structure)
Identification of natural frequency f of mth order mode by using single degree of freedom identification technologym)
In combination with vibration theory, the modal coordinates of X, Y, Z in 3 directions of the complex three-dimensional structure can be derived
Are consistent.
And 204, forming an integral modal response matrix of a three-dimensional structure by the vibration response signal matrix in the X direction, the vibration response signal matrix in the Y direction and the vibration response signal matrix in the Z direction. X, Y, Z vibration response signals in three directions are assembled into an integral module of the whole three-dimensional structureA state response matrix. The overall modal response matrix after assembly can be represented as
(HThree)3H×T(t) is the overall modal response matrix of the overall three-dimensional structure; (X)Three)H×T(t)、(YThree)H×T(t)、(ZThree)H×T(t) X, Y, Z directional vibration response signal matrixes respectively; (phi.)Three)3H×SIs a main mode shape vector of each order of complex three-dimensional structure
The formed mode shape matrix; (Q)Three)S×T(t) is the modal response of each order of the three-dimensional structure
And forming a modal coordinate response matrix.
And step 205, obtaining a modal coordinate response matrix by using a Laplace feature mapping method according to the overall modal response matrix.
Step 205 specifically includes:
the overall modal response matrix is
Wherein (X)Three)H×T(t) represents a vibration response signal matrix in the X direction, (Y)Three)H×T(t) a vibration response signal matrix in the Y direction, (Z)Three)H×T(t) represents a vibration response signal matrix in the Z direction.
Obtaining the nearest K of each X-direction time domain vibration response signal in the vibration response signal matrix in the X directionXAdjacent X-direction time domain vibration response signals, and K nearest to each Y-direction time domain vibration response signal in vibration response signal matrix in Y directionYThe time domain vibration response signals in the adjacent Y direction and each time domain vibration response signal in the Z direction in the vibration response signal matrix away from the Z directionNear KZAnd the adjacent Z-direction time domain vibration response signals.
And reconstructing the X-direction local structural characteristics of the X-direction time domain vibration response signal matrix by using the weights of all the adjacent X-direction time domain vibration response signals. The method specifically comprises the following steps:
according to jXTime domain vibration response signal in X direction and distance jXThe k-th nearest to the X-direction time domain vibration response signalXDetermining j th time domain vibration response signal in X direction through Gaussian kernel functionXThe time domain vibration response signal in the X direction and the kthXWeights of the adjacent X-direction time domain vibration response signals; k is a radical ofX＝1,2,...,KX。
And all the X-direction time domain vibration response signals and the weights of the adjacent X-direction time domain vibration response signals corresponding to the X-direction time domain vibration response signals form an X-direction adjacency matrix.
According to jXThe time domain vibration response signal in the X direction and the kthXThe weight of the time domain vibration response signal in the adjacent X direction is calculated by formula
Determining an X-direction degree matrix; the X-direction degree matrix is composed of
A diagonal matrix is formed; wherein the content of the first and second substances,
denotes the j (th)XThe degree of the X-direction time-domain vibration response signal,
denotes the j (th)XThe time domain vibration response signal in the X direction and the kthXWeights of the adjacent X-direction time domain vibration response signals; the X-direction local structural feature of the X-direction time domain vibration response signal matrix comprises an X-direction degree matrix and an X-direction Laplace matrix.
According to the X-direction adjacency matrix and the X-direction degree matrix, the formula LX＝DX-WXDetermining an X-direction Laplace matrix; wherein L isXDenotes the X-direction Laplace matrix, DXRepresenting the X-direction degree matrix, WXRepresenting an X-direction adjacency matrix.
And reconstructing the Y-direction local structural feature of the Y-direction time domain vibration response signal matrix by using the weights of all adjacent Y-direction time domain vibration response signals.
And reconstructing the Z-direction local structural feature of the Z-direction time domain vibration response signal matrix by using the weights of all adjacent Z-direction time domain vibration response signals.
Respectively carrying out eigenvalue decomposition on the X-direction local structural feature, the Y-direction local structural feature and the Z-direction local structural feature by using a Laplace feature mapping method to obtain dXX-direction feature vector corresponding to minimum non-zero eigenvalue of X-direction local structural feature decomposition, dYY-direction feature vector corresponding to minimum non-zero eigenvalue of local structure feature decomposition in Y-direction, dZAnd the Z-direction characteristic vector corresponding to the minimum non-zero characteristic value of the Z-direction local structural characteristic decomposition.
dXForming an X-direction time domain vibration response signal dimension reduction matrix by the X-direction characteristic vectors, dYForming a Y-direction time domain vibration response signal dimension reduction matrix by the Y-direction characteristic vectors, dZForming a Z-direction time domain vibration response signal dimension reduction matrix by the Z-direction characteristic vectors; the modal response matrix in the X direction corresponds to the dimension reduction matrix of the time domain vibration response signals in the X direction, the modal response matrix in the Y direction corresponds to the dimension reduction matrix of the time domain vibration response signals in the Y direction, and the modal response matrix in the Z direction corresponds to the dimension reduction matrix of the time domain vibration response signals in the Z direction.
And forming a modal coordinate response matrix by the modal response matrix in the X direction, the modal response matrix in the Y direction and the modal response matrix in the Z direction.
And step 206, obtaining a modal shape matrix by using a least square method generalized inverse method according to the modal coordinate response matrix.
Step 206 specifically includes:
using a minimum of two according to the modal coordinate response matrixGeneralized inverse method of multiplication
Solving to obtain a modal shape matrix; wherein (phi)Three)3H×SRepresents a mode shape matrix, (H)Three)3H×T(t) represents the overall modal response matrix, (Q)Three)S×T(t) represents a modal coordinate response matrix,
a transpose matrix representing a modal coordinate response matrix.
And step 207, obtaining the modal natural frequency by utilizing a single degree of freedom technology or a Fourier transform method according to the modal coordinate response matrix.
According to the modal coordinate response matrix, obtaining the modal natural frequency by using a Fourier transform method, which specifically comprises the following steps:
substituting the modal coordinate response matrix into a Fourier transform formula
Obtaining frequency domain data; the largest frequency value in the frequency domain data is the modal natural frequency.
The present embodiment further provides an apparatus fault diagnosis method, which performs fault diagnosis and health status monitoring on an apparatus by using the working mode parameter identification method, and fig. 3 is a flowchart of the apparatus fault diagnosis method provided in the embodiment of the present invention. Referring to fig. 3, the apparatus fault diagnosis method includes:
a set of multi-channel vibrational response data is collected by a vibration sensor disposed in the device to be diagnosed.
In step 305, if the first determination result is yes, the device to be diagnosed has no fault.
And step 306, if the first judgment result is negative, the equipment to be diagnosed has a fault.
According to the equipment fault diagnosis and health state monitoring method, the plurality of vibration sensor devices are arranged on the structural key points of the equipment to be diagnosed, working modal parameters are identified through vibration response signals measured by the vibration sensors, and modal parameters of the equipment to be diagnosed are detected.
In this embodiment, the method for identifying the working modal parameters of the three-dimensional structure is applied to the three-dimensional cylindrical shell, and the modal parameters of the three-dimensional cylindrical shell are identified:
referring to fig. 4, a three-dimensional cylindrical shell is placed on two bases spaced apart, an excitation device is placed in the space between the two bases, and a baffle is placed on each of the two bottom surfaces of the cylindrical shell. X, Y and Z in FIG. 4 are coordinate axes of a rectangular spatial coordinate system. The parameters of the three-dimensional cylindrical shell are as follows: the cylindrical shell is made of a material having a thickness of 0.005 m, a radius of 0.1825 m and a total length of 0.37 m, and has an elastic modulus of 205GPa, a Poisson ratio of 0.3 and a density of 7850kg/m3. In the process of modal parameter identification, the damping ratios eta of 0.03, 0.05 and 0.1 are artificially set respectively for modal parameter identification. The observation points of the vibration sensors on the cylindrical shell are arranged in the following rule: first, the cylindrical shell is divided axially uniformly into 38 turns along its length, and then 115 observation points are arranged uniformly in each turn, so that a total of H38 × 115 4370 vibration sensor observation points are arranged on the surface of the cylindrical shell. After the vibration sensor is arranged, Gaussian white noise excitation is applied to the cylindrical shell by using an excitation device, and the three-dimensional cylindrical shell is obtained by samplingThe vibration response signal of (1). Wherein, the sampling frequency of the signal acquisition equipment is set to 5120Hz, and the time length of the sampling is set to 1 second, namely T is 5120.
Performing modal parameter identification on the three-dimensional cylindrical shell by using a working modal parameter identification method of a three-dimensional structure to obtain a modal coordinate response matrix (Q)Three)S×T(t) and responding to the modal coordinates with a matrix (Q)Three)S×T(t) performing FFT to obtain modal natural frequency, wherein the modal natural frequency of the three-dimensional cylindrical shell at 1 st, 2 nd, 3 rd, 4 th and 7 th orders is shown in figure 5; response matrix (Q) according to modal coordinatesThree)S×T(t) obtaining a mode shape matrix by using a least square method generalized inverse method, wherein the mode shapes of the three-dimensional cylindrical shell in the 1 st, 2 nd, 3 rd, 4 th and 7 th orders are shown in fig. 6(b), and the real mode shapes of the three-dimensional cylindrical shell in the 1 st, 2 nd, 3 rd, 4 th and 7 th orders are shown in fig. 6(a) and numbers marked in fig. 6 represent the fluctuation range of the signals.
The confidence coefficient of the working mode parameter identification method (LE method) based on the laplace feature mapping of the present invention is shown in table 1, and table 1 is the confidence coefficient of the working mode parameter identification method based on the laplace feature mapping of the present invention in the 1 st, 2 nd, 3 th, 4 th and 7 th orders.
TABLE 1
The modal natural frequencies identified by the LE method of the present invention are referred to in table 2. The relative error rate of the LE method is the relative error between the modal natural frequency solved by the LE method and the true modal natural frequency. Table 2 shows the true modal natural frequencies at orders 1,2, 3, 4 and 7, and the relative error rates at orders 1,2, 3, 4 and 7 of the working modal parameter identification method based on laplace feature mapping according to the present invention.
TABLE 2
The invention discloses a working modal parameter identification method based on Laplace feature mapping, which applies the Laplace feature mapping in manifold learning to working modal analysis, in particular to a working modal parameter identification method aiming at linear engineering structures and three-dimensional linear engineering structures, and can effectively detect the working modal parameters of the linear engineering structures and the three-dimensional linear engineering structures. The identification precision of the Laplace feature mapping method for identifying the working modal parameters is higher than that of the principal component analysis algorithm for identifying the working modal parameters, and the Laplace feature mapping method has the characteristic of low time and space complexity, because the time overhead of the Laplace matrix L of the construction diagram of the Laplace feature mapping method is low. In addition, the time-varying transient working mode parameters (transient working mode shape and natural frequency of the transient working mode) of the linear time-invariant structure can be identified on line in real time only by actually measuring the non-stationary vibration response signal, and the method has great advantages compared with the traditional test mode parameter identification technology which needs to measure the excitation and response signals at the same time.
The method for identifying the working modal parameters of the three-dimensional structure based on the Laplace feature mapping can effectively identify the working modal parameters (modal shape and modal frequency) of the three-dimensional structure, and can be used for equipment fault diagnosis, health monitoring and structural analysis and optimization. Compared with the working modal parameter identification method using a principal component analysis method, the method can greatly improve the identification precision of the first order and the second order, reduce the time and memory overhead, be more easily used for equipment fault diagnosis, health monitoring and system structure analysis and optimization, and have greater advantages compared with the traditional test modal parameter identification technology which needs to measure excitation and response signals simultaneously.
The embodiments in the present description are described in a progressive manner, each embodiment focuses on differences from other embodiments, and the same and similar parts among the embodiments are referred to each other. For the system disclosed by the embodiment, the description is relatively simple because the system corresponds to the method disclosed by the embodiment, and the relevant points can be referred to the method part for description.
The principles and embodiments of the present invention have been described herein using specific examples, which are provided only to help understand the method and the core concept of the present invention; meanwhile, for a person skilled in the art, according to the idea of the present invention, the specific embodiments and the application range may be changed. In view of the above, the present disclosure should not be construed as limiting the invention.
Claims (10)
1. A working mode parameter identification method is characterized by comprising the following steps:
arranging a plurality of vibration sensors in a one-dimensional structure of which working modal parameters are to be determined; the vibration sensor is used for detecting a time domain vibration response signal of the linear time-invariant system under the excitation of a natural environment within a preset time; the working modal parameters comprise a modal shape and a modal natural frequency;
acquiring a time domain vibration response signal matrix formed by the time domain vibration response signals detected by each vibration sensor within preset time;
obtaining a modal response matrix by utilizing a Laplace characteristic mapping method according to the time domain vibration response signal matrix;
obtaining a modal shape matrix by utilizing a least square method generalized inverse method according to the modal response matrix;
and obtaining the modal natural frequency by utilizing a single degree of freedom technology or a Fourier transform method according to the modal response matrix.
2. The method for identifying working modal parameters according to claim 1, wherein the obtaining a modal response matrix by using a laplacian eigenmap method according to the time-domain vibration response signal matrix specifically comprises:
the time domain vibration response signal matrix is
Wherein
Representing a time domain vibration response signal detected by a jth vibration sensor within a preset time t, wherein n represents the total number of the vibration sensors;
acquiring K adjacent time domain vibration response signals closest to the jth time domain vibration response signal;
reconstructing local structural features of the time domain vibration response signal matrix by using the weights of all the adjacent time domain vibration response signals;
performing eigenvalue decomposition on the local structural characteristics of the time domain vibration response signal matrix by using a Laplace eigenvalue mapping method to obtain d eigenvectors corresponding to the minimum non-zero eigenvalues;
and the eigenvectors corresponding to the d minimum non-zero eigenvalues form a time domain vibration response signal dimension reduction matrix, and the modal response matrix corresponds to the time domain vibration response signal dimension reduction matrix.
3. The method according to claim 2, wherein the reconstructing the local structural feature of the time-domain vibro-responsive signal matrix using the weights of all the adjacent time-domain vibro-responsive signals specifically comprises:
determining the weight of the jth time domain vibration response signal and the kth adjacent time domain vibration response signal through a Gaussian kernel function according to the jth time domain vibration response signal and the kth adjacent time domain vibration response signal which is closest to the jth time domain vibration response signal; k1, 2,. K;
all the time domain vibration response signals and the weights of the adjacent time domain vibration response signals corresponding to the time domain vibration response signals form an adjacency matrix;
according to the weight of the jth time domain vibration response signal and the kth adjacent time domain vibration response signal, the formula is adopted
Determining the degree of the time domain vibration response signal; the degree matrix is a diagonal matrix formed by the degrees of the time domain vibration response signals; wherein the content of the first and second substances,
in the formula, DjkDegree, w, of a j-th time-domain vibration response signaljkRepresenting the weight of the jth time domain vibration response signal and the kth adjacent time domain vibration response signal, wherein sigma represents the width parameter of the Gaussian kernel function; the local structural characteristics of the time domain vibration response signal matrix comprise a degree matrix and a Laplace matrix;
determining a laplacian matrix by a formula L ═ D-W according to the adjacency matrix and the degree matrix; where L denotes a laplacian matrix, D denotes a degree matrix, and W denotes an adjacency matrix.
4. The method for identifying working modal parameters according to claim 1, wherein the obtaining a modal shape matrix by using a least square generalized inverse method according to the modal response matrix specifically comprises:
according to the modal response matrix, utilizing a least square generalized inverse method phi ═ X (t) QT(t)(Q(t)QT(t))-1Solving to obtain a modal shape matrix; wherein Φ represents a mode shape matrix, x (t) represents a time domain vibration response signal matrix, and q (t) represents a mode response matrix.
5. The method for identifying working modal parameters according to claim 1, wherein obtaining modal natural frequencies by using a fourier transform method according to the modal response matrix specifically comprises:
substituting the modal response matrix into a Fourier transform formula
Obtaining frequency domain data; the maximum frequency value in the frequency domain data is the modal natural frequency.
6. A working mode parameter identification method is characterized by comprising the following steps:
arranging a plurality of vibration sensors in a three-dimensional structure of which working modal parameters are to be determined; the vibration sensor is used for detecting a time domain vibration response signal of the linear time-invariant system under the excitation of a natural environment within a preset time; the working modal parameters comprise a modal shape and a modal natural frequency;
acquiring a three-dimensional time domain vibration response signal matrix formed by the time domain vibration response signals detected by each vibration sensor within preset time;
discretizing the three-dimensional time domain vibration response signal matrix to obtain a vibration response signal matrix in the X direction, a vibration response signal matrix in the Y direction and a vibration response signal matrix in the Z direction; x, Y and Z are coordinate axes of a space rectangular coordinate system;
forming an integral modal response matrix of the three-dimensional structure by the vibration response signal matrix in the X direction, the vibration response signal matrix in the Y direction and the vibration response signal matrix in the Z direction;
obtaining a modal coordinate response matrix by utilizing a Laplace characteristic mapping method according to the overall modal response matrix;
obtaining a modal shape matrix by utilizing a least square method generalized inverse method according to the modal coordinate response matrix;
and obtaining the modal natural frequency by utilizing a single degree of freedom technology or a Fourier transform method according to the modal coordinate response matrix.
7. The method for identifying working modal parameters according to claim 6, wherein the obtaining a modal coordinate response matrix by using a laplace feature mapping method according to the overall modal response matrix specifically comprises:
the overall modal response matrix is
Wherein (X)Three)H×T(t) in the X directionVibration response signal matrix, (Y)Three)H×T(t) a vibration response signal matrix in the Y direction, (Z)Three)H×T(t) a matrix of vibration response signals representing the Z direction;
obtaining the K nearest to each X-direction time domain vibration response signal in the vibration response signal matrix in the X directionXAdjacent X-direction time domain vibration response signals, and K nearest to each Y-direction time domain vibration response signal in the vibration response signal matrix in the Y directionYAdjacent time domain vibration response signals in Y direction and K nearest to each time domain vibration response signal in Z direction in vibration response signal matrix in Z directionZTime domain vibration response signals in adjacent Z directions;
reconstructing the X-direction local structural feature of the X-direction time domain vibration response signal matrix by using the weights of all the adjacent X-direction time domain vibration response signals;
reconstructing Y-direction local structural features of the Y-direction time domain vibration response signal matrix by using the weights of all the adjacent Y-direction time domain vibration response signals;
reconstructing Z-direction local structural features of the Z-direction time domain vibration response signal matrix by using the weights of all the adjacent Z-direction time domain vibration response signals;
respectively carrying out eigenvalue decomposition on the X-direction local structural feature, the Y-direction local structural feature and the Z-direction local structural feature by utilizing a Laplace feature mapping method to obtain dXThe X-direction characteristic vector, d, corresponding to the minimum non-zero eigenvalue of the X-direction local structural characteristic decompositionYY-direction feature vector d corresponding to minimum non-zero eigenvalue of Y-direction local structural feature decompositionZZ-direction feature vectors corresponding to the minimum non-zero eigenvalues of the Z-direction local structural feature decomposition;
dXforming an X-direction time domain vibration response signal dimension reduction matrix by the X-direction characteristic vectors, dYForming a Y-direction time domain vibration response signal dimension reduction matrix by the Y-direction characteristic vectors, dZThe Z-direction characteristic vector forms a Z-direction time domain vibration response signalReducing the dimension matrix; the modal response matrix in the X direction corresponds to the dimension reduction matrix of the time domain vibration response signal in the X direction, the modal response matrix in the Y direction corresponds to the dimension reduction matrix of the time domain vibration response signal in the Y direction, and the modal response matrix in the Z direction corresponds to the dimension reduction matrix of the time domain vibration response signal in the Z direction;
and forming a modal coordinate response matrix by the modal response matrix in the X direction, the modal response matrix in the Y direction and the modal response matrix in the Z direction.
8. The method according to claim 7, wherein the reconstructing the X-direction local structural feature of the X-direction time-domain vibration response signal matrix by using the weights of all the adjacent X-direction time-domain vibration response signals specifically comprises:
according to jXThe time domain vibration response signal in the X direction and the distance jXThe k-th nearest to the X-direction time domain vibration response signalXDetermining j th time domain vibration response signal in X direction through Gaussian kernel functionXThe time domain vibration response signal in the X direction and the kthXWeights of the adjacent X-direction time domain vibration response signals; k is a radical ofX＝1,2,...,KX；
All the X-direction time domain vibration response signals and the weights of the adjacent X-direction time domain vibration response signals corresponding to the X-direction time domain vibration response signals form an X-direction adjacency matrix;
according to jXThe time domain vibration response signal in the X direction and the kthXThe weight of the time domain vibration response signal in the adjacent X direction is calculated by formula
Determining an X-direction degree matrix; the X-direction degree matrix is composed of
A diagonal matrix is formed; wherein the content of the first and second substances,
denotes the j (th)XThe degree of the X-direction time-domain vibration response signal,
denotes the j (th)XThe time domain vibration response signal in the X direction and the kthXWeights of the adjacent X-direction time domain vibration response signals; the X-direction local structural characteristics of the X-direction time domain vibration response signal matrix comprise an X-direction degree matrix and an X-direction Laplace matrix;
according to the X-direction adjacency matrix and the X-direction degree matrix, a formula L is obtainedX＝DX-WXDetermining an X-direction Laplace matrix; wherein L isXDenotes the X-direction Laplace matrix, DXRepresenting the X-direction degree matrix, WXRepresenting an X-direction adjacency matrix.
9. The method for identifying working modal parameters according to claim 6, wherein the obtaining a modal shape matrix by using a least square generalized inverse method according to the modal coordinate response matrix specifically comprises:
according to the modal coordinate response matrix, utilizing least square method generalized inverse method
Solving to obtain a modal shape matrix; wherein (phi)Three)3H×SRepresents a mode shape matrix, (H)Three)3H×T(t) represents the overall modal response matrix, (Q)Three)S×T(t) represents a modal coordinate response matrix,
a transpose matrix representing a modal coordinate response matrix.
10. An apparatus fault diagnosis method, comprising:
if the equipment to be diagnosed is of a one-dimensional structure, determining the working modal parameters of the equipment to be diagnosed at the current moment by using the working modal parameter identification method according to any one of claims 1 to 5;
if the equipment to be diagnosed is of a three-dimensional structure, determining the working mode parameters of the equipment to be diagnosed at the current moment by using the working mode parameter identification method according to any one of claims 6 to 9;
obtaining working mode parameters of the equipment to be diagnosed at the last moment;
judging whether the determined working modal parameter of the equipment to be diagnosed at the current moment is completely consistent with the working modal parameter of the equipment to be diagnosed at the last moment or not to obtain a first judgment result;
if the first judgment result is yes, the equipment to be diagnosed has no fault;
and if the first judgment result is negative, the equipment to be diagnosed has a fault.
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