A method and system for identifying complex modal parameters of a current-carrying pipeline

Abstract

The present invention belongs to the technical field of working mode analysis, and discloses a method and system for identifying complex modal parameters of a current-carrying pipeline. The present invention obtains the vibration responses of a number of measuring points on the current-carrying pipeline under load excitation; calculates the vibration response correlation functions of each measuring point and a reference point; uses variational mode decomposition to decompose the vibration response correlation functions into a series of independent intrinsic mode functions; divides the intrinsic mode functions into two categories: intrinsic mode functions with varying amplitudes and constant amplitudes; eliminates the intrinsic mode functions with constant amplitudes, and establishes an intrinsic mode function matrix; performs a Hilbert transform on the intrinsic mode function matrix, and combines the intrinsic mode function matrix with its Hilbert transform matrix to obtain a signal analytical matrix; based on the signal analytical matrix, identifies the amplitudes and phases of the complex modal shapes of the current-carrying pipeline, as well as the natural frequencies and damping ratios of the current-carrying pipeline. The present invention can identify the complex modal parameters of the current-carrying pipeline under operating conditions.

Description

Technical Field

[0001] The present invention belongs to the technical field of operational modal analysis, and more specifically, relates to a method and system for identifying complex modal parameters of a current-carrying pipeline. Background Art

[0002] With the gradual increase in the energy density of power equipment, higher requirements are put forward for the dynamic performance of current-carrying pipelines in various fields. During actual operation, the current-carrying pipeline may have problems of excessive local or overall vibration, inducing fatigue damage of the pipeline, increasing its leakage risk, and affecting the overall safety and stability of the system. In order to ensure the safety of the current-carrying pipeline, scientific and reasonable testing and signal processing means need to be adopted to establish a long-term health monitoring system for the in-service pipeline, and to analyze and evaluate the dynamic performance of the pipeline in the operating state in real time. Generally speaking, the dynamic characteristics of industrial structures can be described by three key modal parameters, namely, natural frequency, damping ratio, and modal shape. These modal parameters can usually be obtained through two methods: experimental modal analysis and operational modal analysis. Experimental modal analysis is to apply an excitation force to the test structure through a force hammer or an exciter, and identify the modal parameters from the frequency response function of the structure. This method usually requires knowing the magnitude and position of the pure external force excitation applied to the structure. Operational modal analysis is to directly use the vibration response generated by internal or external excitation of the structure in the operating state to identify the vibration response of the structure. The advantage of this method is that it does not require knowing the load form and magnitude of the structure, so it is widely used in the fields of structural health monitoring, condition assessment, and intelligent control. For engineering current-carrying pipelines, due to the static pressure deformation of the pipeline and the flow of internal fluid caused by the power equipment during operation, there may be significant differences in the geometric shape and system parameters of the same current-carrying pipeline between the operating state and the non-operating state. Therefore, it is difficult to invert or characterize the dynamic performance of the current-carrying pipeline in the operating state based on the experimental modal analysis results in the non-operating state. In addition, due to the interference of the operating excitation of the power equipment connected to the pipeline during the operating state, it is difficult to carry out experimental modal analysis on the pipeline during the operating stage to obtain its modal parameters. Therefore, the operational mode shape analysis method has become the key method for analyzing and evaluating the dynamic performance of current-carrying pipelines with operating excitation interference.

[0003] Due to the influence of the Coriolis force and centrifugal force caused by the fluid flow in the pipe, the modal vibration mode of the operating pipeline is generally a complex modal vibration mode. The existing methods are less efficient in the identification and calculation of the working vibration mode of the current-carrying pipeline, and it is even difficult to obtain the accurate complex modal vibration mode of the current-carrying pipeline. For the problem of identifying the complex modal parameters of the structure, the most commonly used method currently is the time-frequency analysis method based on the Hilbert transform. This method extracts the instantaneous amplitude and phase from the vibration response data obtained by testing through the Hilbert transform, and then uses the polynomial fitting technique to identify the modal frequency, damping ratio, response amplitude, and initial phase of the structure. This method is effective for a single-degree-of-freedom system or a multi-degree-of-freedom system with low modal coupling, but it is difficult to work for a complex system with dense modes or high modal coupling. Therefore, it is necessary to establish a method for identifying the complex modal parameters of a current-carrying pipeline under working condition loads (random excitation and harmonic excitation). Summary of the Invention

[0004] The present invention provides a method and system for identifying the complex modal parameters of a current-carrying pipeline, which solves the problem that it is difficult to identify the complex modal parameters of the current-carrying pipeline in the operating state in the prior art.

[0005] The present invention provides a method for identifying the complex modal parameters of a current-carrying pipeline, comprising the following steps:

[0006] Obtain the vibration responses of several measuring points on the current-carrying pipeline under load excitation;

[0007] Select a reference point and calculate the cross-correlation function of the vibration responses of each measuring point and the reference point;

[0008] Use variational mode decomposition to decompose the cross-correlation function of the vibration response under the combined excitation of harmonic load and random load into a series of independent intrinsic mode functions;

[0009] Classify the intrinsic mode functions into two categories: intrinsic mode functions with varying amplitudes corresponding to random load excitation and intrinsic mode functions with constant amplitudes corresponding to harmonic load excitation;

[0010] Eliminate the intrinsic mode functions with constant amplitudes, and establish an intrinsic mode function matrix; perform the Hilbert transform on the intrinsic mode function matrix, and combine the intrinsic mode function matrix with its Hilbert transform matrix to obtain a signal analysis matrix;

[0011] Based on the signal analysis matrix, identify the amplitude and phase of the complex modal vibration mode of the current-carrying pipeline, as well as the natural frequency and damping ratio of the current-carrying pipeline.

[0012] Preferably, the vibration responses of the measuring points under load excitation are obtained by arranging velocity sensors or acceleration sensors on the current-carrying pipeline.

[0013] Preferably, a measurement point on the current-carrying pipeline with a vibration response greater than the first threshold and a number of modal peaks greater than the second threshold is selected as a reference point.

[0014] Preferably, the variational mode decomposition decomposes the vibration response correlation function into a superposition of a series of amplitude-modulated and frequency-modulated signals. The variational mode decomposition establishes a constrained variational problem, transforms the constrained variational problem into an unconstrained variational problem through the augmented Lagrangian function, and uses the multiplicative operator alternating direction method to solve for the optimal solution to obtain the intrinsic mode function and its corresponding central frequency.

[0015] Preferably, after each iteration update of the intrinsic mode function and the central frequency, the Lagrangian multiplication operator is updated first, and then the iteration is continued until the convergence condition is met.

[0016] Preferably, the set composed of the intrinsic mode functions with varying amplitudes is expressed as: ;

[0017] Wherein, ;

[0018] In the formula, is the i th intrinsic mode function with varying amplitude, is the amplitude of the i th intrinsic mode function with varying amplitude, is the amplitude constant of the i th intrinsic mode function with varying amplitude, is the i th order damping ratio, is the i th order natural frequency, T is the time delay, is the phase of the i th intrinsic mode function with varying amplitude, p represents the measurement point, q represents the reference point, i = 1, 2,..., , is the number of intrinsic mode functions with varying amplitudes;

[0019] The set composed of the intrinsic mode functions with constant amplitudes is expressed as: :

[0020] Wherein, ;

[0021] In the formula, is the h th intrinsic mode function with constant amplitude, is the amplitude of the h th intrinsic mode function with constant amplitude, is the phase of the h th intrinsic mode function with a constant amplitude, h = 1, 2, ……, , is the number of intrinsic mode functions with a constant amplitude, , K is the total number of intrinsic mode functions.

[0022] Preferably, the element in the p th row and i th column of the intrinsic mode function matrix is expressed as:

[0023]

[0024] wherein, is the element in the p th row and i th column of the intrinsic mode function matrix, p = 1, 2, ……, , is the total number of measurement points, i = 1, 2, ……, , is the number of intrinsic mode functions with a varying amplitude; q represents the reference point;

[0025] The element in the p th row and i th column of the signal analysis matrix is expressed as:

[0026]

[0027] wherein, ;

[0028] wherein, is the element in the p th row and i th column of the signal analysis matrix;

[0029] In the expressions of the intrinsic mode function matrix and the signal analysis matrix, is the amplitude of the element in the p th row and i th column of the matrix, is the amplitude constant of the element in the p th row and i th column of the matrix, is the i th damping ratio, is the i th natural frequency, is the p th row andi The phase of the element in the column;

[0030] Wherein, , is the i th-order modal frequency; is the degree of freedom p and q The phase difference of the vibration response correlation function at the frequency .

[0031] Preferably, the complex modal vibration mode of the current-carrying pipeline is expressed as:

[0032]

[0033] In the formula, is the complex modal vibration mode of the current-carrying pipeline, is the amplitude matrix of the complex modal vibration mode of the current-carrying pipeline, is the phase matrix of the complex modal vibration mode of the current-carrying pipeline;

[0034] Taking q the degree of freedom as the reference point, the element in the th p row and the i th column is expressed as: , and the elements in the q th row of

[0035] Taking q the degree of freedom as the reference point, the element in the th p row and the i th column is expressed as: , and the elements in the q th row of

[0036] In the formula, is the element in the p th i row and the p th column of i indicating the amplitude of the th-order modal vibration mode of the q th degree of freedom on the current-carrying pipeline; i is the amplitude constant of the element in the

[0037] is the element in the p th i row and the indicating the p th degree of freedom on the current-carrying pipelinei The phase of the first-order modal vibration mode; as the reference point q The phase difference of the autocorrelation function of the vibration response at the frequency at.

[0038] Preferably, if the amplitudes and phases of the complex modal vibration modes of the current-carrying pipeline identified based on the signal analysis matrix are time-varying, they are processed by the linear regression method to obtain the time-invariant amplitudes and phases of the complex modal vibration modes.

[0039] On the other hand, the present invention provides a system for identifying complex modal parameters of a current-carrying pipeline, including:

[0040] A vibration response acquisition module for acquiring the vibration responses of a number of measurement points on the current-carrying pipeline under load excitation;

[0041] A correlation function calculation module for selecting a reference point and calculating the correlation functions of the vibration responses of each measurement point and the reference point;

[0042] A variational mode decomposition module for decomposing the correlation function of the vibration response under the combined excitation of harmonic load and random load into a series of independent intrinsic mode functions by using variational mode decomposition;

[0043] A classification module for classifying the intrinsic mode functions into two categories: intrinsic mode functions with varying amplitudes corresponding to random load excitation and intrinsic mode functions with constant amplitudes corresponding to harmonic load excitation;

[0044] A matrix construction module for removing the intrinsic mode functions with constant amplitudes, establishing an intrinsic mode function matrix; and for performing Hilbert transform on the intrinsic mode function matrix and combining the intrinsic mode function matrix with its Hilbert transform matrix to obtain a signal analysis matrix;

[0045] An identification module for identifying the amplitudes and phases of the complex modal vibration modes of the current-carrying pipeline, as well as the natural frequency and damping ratio of the current-carrying pipeline, based on the signal analysis matrix;

[0046] The system for identifying complex modal parameters of the current-carrying pipeline is used to execute the steps in the above-mentioned method for identifying complex modal parameters of the current-carrying pipeline.

[0047] One or more technical solutions provided in the present invention have at least the following technical effects or advantages:

[0048] To solve the problems of random noise and harmonic mode interference in the complex modal analysis of the operation of current-carrying pipelines and to realize the identification of complex modal parameters under the operating state of current-carrying pipelines, the complex modal parameter identification scheme proposed in the present invention first obtains the vibration responses of several measuring points on the current-carrying pipeline under load excitation, calculates the vibration response correlation functions of each measuring point and the reference point, and then uses variational mode decomposition to decompose the vibration response correlation function under the combined excitation of harmonic load and random load into a series of independent intrinsic mode functions; then the intrinsic mode functions are divided into two categories: intrinsic mode functions with varying amplitudes corresponding to random load excitation and intrinsic mode functions with constant amplitudes corresponding to harmonic load excitation; then the intrinsic mode functions with constant amplitudes are removed to establish an intrinsic mode function matrix; the Hilbert transform is performed on the intrinsic mode function matrix, and the intrinsic mode function matrix and its Hilbert transform matrix are combined to obtain a signal analysis matrix; finally, the amplitudes and phases of the complex modal shapes of the current-carrying pipeline, as well as the natural frequencies and damping ratios of the current-carrying pipeline, are identified based on the signal analysis matrix.

[0049] The present invention transforms the problem of identifying the operating modal parameters of current-carrying pipelines into the problem of decomposing and analyzing the vibration response correlation functions of pipelines. The variational mode decomposition technique is used to decompose the vibration response correlation function into a series of independent intrinsic mode components composed of structural modal components and harmonic components. Based on the characteristics and differences of the vibration response correlation functions under two types of load excitations obtained through theoretical derivation, the harmonic components are removed from the decomposed intrinsic mode components. On this basis, the Hilbert transform method is introduced to obtain the instantaneous amplitude and phase of each structural modal component, and the frequencies, damping ratios, response amplitudes, and phases corresponding to each mode are extracted therefrom. The complex modal shape of the current-carrying pipeline under the working state can be obtained through the transfer function analysis method.

[0050] As the first method for identifying the complex modal parameters of operating current-carrying pipelines, on the one hand, the method proposed in the present invention can effectively eliminate the influence of harmonic excitation during the operation of pipelines without increasing the dimension of the calculation process matrix, avoid false modes in modal parameter identification caused by harmonic responses, and enhance the reliability of the identification results; on the other hand, it analyzes the vibration response correlation function into independent amplitude functions and phase functions through the Hilbert transform, and respectively identifies the amplitudes and phases of the complex modal shapes of the current-carrying pipeline, avoiding the influence of the large accumulation of real part identification errors on the identification results of the smaller imaginary part during the simultaneous identification of the real and imaginary parts of the traditional complex modal shape, and increasing the accuracy of the identification results of the complex modal shape; in addition, by introducing the correlation function and variational mode decomposition, the measurement error of the pipeline vibration response and the phase noise of the vibration response induced by random excitation can be greatly suppressed, and the stability and robustness of the identification results are also enhanced. Description of the Drawings

[0051] Figure 1Flow chart of a method for identifying complex modal parameters of a current-carrying pipeline provided by an embodiment of the present invention. Detailed implementation manners

[0052] To better understand the above technical solution, the above technical solution will be described in detail below in conjunction with the accompanying drawings of the specification and specific implementation manners.

[0053] Embodiment 1:

[0054] Embodiment 1 provides a method for identifying complex modal parameters of a current-carrying pipeline. Refer to Figure 1 , which includes the following steps:

[0055] Obtain the vibration responses of several measuring points on the current-carrying pipeline under load excitation;

[0056] Select a reference point and calculate the vibration response correlation functions between each measuring point and the reference point;

[0057] Using variational mode decomposition, decompose the vibration response correlation function under the combined excitation of harmonic load and random load into a series of independent intrinsic mode functions;

[0058] Classify the intrinsic mode functions into two categories: intrinsic mode functions with varying amplitudes corresponding to random load excitation and intrinsic mode functions with constant amplitudes corresponding to harmonic load excitation;

[0059] Eliminate the intrinsic mode functions with constant amplitudes, establish an intrinsic mode function matrix; perform Hilbert transform on the intrinsic mode function matrix, and combine the intrinsic mode function matrix with its Hilbert transform matrix to obtain a signal analytic matrix;

[0060] Based on the signal analytic matrix, identify the amplitudes and phases of the complex modal shapes of the current-carrying pipeline, as well as the natural frequencies and damping ratios of the current-carrying pipeline.

[0061] Among them, the vibration responses of the measuring points under load excitation can be obtained by arranging velocity sensors or acceleration sensors on the current-carrying pipeline for testing.

[0062] The measuring points on the current-carrying pipeline with vibration responses greater than the first threshold and the number of modal peaks greater than the second threshold can be selected as the reference points.

[0063] The variational mode decomposition decomposes the vibration response correlation function into a superposition of a series of amplitude-modulated and frequency-modulated signals. The variational mode decomposition establishes a constrained variational problem, transforms the constrained variational problem into an unconstrained variational problem through an augmented Lagrangian function, and uses the multiplicative operator alternating direction method to solve for the optimal solution to obtain the intrinsic mode functions and their corresponding central frequencies. After each iteration update of the intrinsic mode functions and central frequencies, first update the Lagrangian multiplicative operator, and then continue to perform the iteration until the convergence condition is satisfied.

[0064] Specifically, the set composed of the intrinsic mode functions with varying amplitudes is expressed as: ;

[0065] where ;

[0066] In the formula, is the i -th intrinsic mode function with varying amplitude, is the amplitude of the i -th intrinsic mode function with varying amplitude, is the amplitude constant of the i -th intrinsic mode function with varying amplitude, is the i -th damping ratio, is the i -th natural frequency, T is the time delay, is the phase of the i -th intrinsic mode function with varying amplitude, p represents the measurement point, q represents the reference point, i = 1, 2, …, , is the number of intrinsic mode functions with varying amplitudes.

[0067] The set composed of the intrinsic mode functions with constant amplitudes is expressed as: :

[0068] where ;

[0069] In the formula, is the h -th intrinsic mode function with constant amplitude, is the amplitude of the h -th intrinsic mode function with constant amplitude, is the phase of the h -th intrinsic mode function with constant amplitude, h = 1, 2, …, , is the number of intrinsic mode functions with constant amplitudes, , K is the total number of intrinsic mode functions.

[0070] Specifically, the element in the p -th row and i -th column of the intrinsic mode function matrix is expressed as:

[0071]

[0072] In the formula, is the element in the p th row and i th column of the intrinsic mode function matrix, p m = 1, 2, ……, , is the total number of measurement points, i n = 1, 2, ……, , is the number of intrinsic mode functions with varying amplitudes; q represents the reference point.

[0073] The element in the p th row and i th column of the signal analysis matrix is expressed as:

[0074]

[0075] where, ;

[0076] In the formula, is the element in the p th row and i th column of the signal analysis matrix.

[0077] In the expressions of the intrinsic mode function matrix and the signal analysis matrix, is the amplitude of the element in the p th row and i th column of the matrix, is the amplitude constant of the element in the p th row and i th column of the matrix, is the i th damping ratio, is the i th natural frequency, is the phase of the element in the p th row and i th column of the matrix.

[0078] where, , is the i th modal frequency, is the phase difference between the p th degree of freedom and the q vibration response correlation function at the frequency .

[0079] Specifically, the complex modal vibration mode of the current-carrying pipeline is expressed as:

[0080]

[0081] In the formula, is the complex modal vibration mode of the current-carrying pipeline, is the amplitude matrix of the complex modal vibration mode of the current-carrying pipeline, is the phase matrix of the complex modal vibration mode of the current-carrying pipeline.

[0082] Taking q degrees of freedom as the reference point, we obtain The element in the p th row and i th column is expressed as: , and All the elements in the q th row of

[0083] Taking q degrees of freedom as the reference point, we obtain The element in the p th row and i th column is expressed as: , and All the elements in the q th row of

[0084] In the formula, is The element in the p th row and i th column, representing the amplitude of the p th mode vibration mode of the i th degree of freedom on the current-carrying pipeline; is the amplitude constant of the element in the q th row and i th column of the matrix;

[0085] is The element in the p th row and i th column of representing the phase of the p th mode vibration mode of the i th degree of freedom on the current-carrying pipeline; is the phase difference of the autocorrelation function of the vibration response of the reference point q at frequency ;

[0086] In addition, if the amplitudes and phases of the complex modal vibration modes of the current-carrying pipeline identified based on the signal analysis matrix are time-varying, they are processed by the linear regression method to obtain the time-invariant amplitudes and phases of the complex modal vibration modes.

[0087] Next, the present invention will be further described as a whole.

[0088] Step 1: Obtain the vibration responses of several measuring points on the current-carrying pipeline under load excitation.

[0089] For any given operating current-carrying pipeline system in practical engineering, a series of velocity or acceleration sensors can be arranged to measure the vibration responses of each measuring point on the pipeline under the excitation of operating loads.

[0090] Step 2: Select a reference point and calculate the correlation function of the vibration responses between each measuring point and the reference point.

[0091] Solve the correlation function of the vibration responses between each measuring point (i.e., at each position, denoted as p ) and the reference point (denoted as q ). .

[0092] In particular, the reference point can be selected according to the spectral characteristics of the vibration responses at each position, choosing the position with large vibration responses and a large number of modal peaks.

[0093] Step 3: Use variational mode decomposition to decompose the correlation function of the vibration responses under the combined excitation of harmonic loads and random loads into a series of independent intrinsic mode functions.

[0094] Use the variational mode decomposition method (VMD) to perform variational mode decomposition on the correlation function of the vibration response of each measuring point to separate the harmonic components and system modal components in the correlation function of the current-carrying pipeline vibration response, and obtain a series of independent intrinsic mode functions . The specific steps of variational mode decomposition are as follows:

[0095] For the calculated correlation function of the vibration responses, it can be decomposed into a superposition of a series of amplitude-modulated and frequency-modulated signals by using the variational mode decomposition method, that is can be approximately expressed as:

[0096]

[0097] where is the intrinsic mode function to be solved; K is the total number of intrinsic mode functions, is 's instantaneous amplitude, is 's instantaneous phase, is 's instantaneous central frequency. and Compared with are slowly varying.

[0098] 1) In the VMD method, the intrinsic mode function and its central frequency can be obtained by solving the following variational problem:

[0099]

[0100] In the formula, is K a set of intrinsic mode functions to be solved, and is the set of center frequencies corresponding to this set; is the partial derivative with respect to the time delay T , is the Dirichlet function, and is the convolution symbol.

[0101] 2) To solve the optimal solution of the constrained variational problem in Equation (2), the Lagrange multiplier operator and the quadratic penalty factor υ are introduced to transform it into an unconstrained variational problem. The extended Lagrangian expression is as follows:

[0102] (3)

[0103] In the formula, is the extended Lagrangian expression, represents the inner product of two vectors.

[0104] 3) Use the Alternate Direction Method of Multipliers (ADMM) to solve the optimal solution of Equation (3). Preset the number of intrinsic modes, and each mode component and its center frequency can be obtained through iterative calculation. Taking the th mode component as an example, its intrinsic mode function and the corresponding center frequency can be obtained through the following formulas (4) and (5).

[0105]

[0106] Among them, , and respectively represent , and 's Fourier transforms, n is the number of iterations.

[0107] Based on the above description, it can be seen that the present invention uses the variational mode decomposition to establish a constrained variational problem, transforms the constrained variational problem into an unconstrained variational problem through the augmented Lagrangian function, and uses the Alternate Direction Method of Multipliers to solve the optimal solution to obtain a set of intrinsic mode functions.

[0108] 4) After each iteration update of the mode and the center frequency, the Lagrange multiplier operator can be updated according to the following formula:

[0109]

[0110] Among them, is the noise tolerance. To obtain a better noise reduction effect, the present invention sets = 10 -8 .

[0111] 5) Continue the above iteration until the convergence condition is met, that is:

[0112]

[0113] wherein, ε is the convergence determination criterion, and the present invention takes ε = 1×10 -7 .

[0114] After variational mode decomposition, the correlation function of the vibration response under the combined excitation of harmonic load and random load can be approximately expressed as a linear superposition of a series of orthogonal intrinsic mode functions.

[0115] That is, step three is mainly used for the decomposition of the correlation function of the measured pipeline vibration response, and the correlation function of the vibration response of the multi-line spectrum of the pipeline is decomposed into a series of independent intrinsic mode functions.

[0116] Step four: Divide the intrinsic mode functions into two categories: the intrinsic mode functions with varying amplitudes corresponding to random load excitation and the intrinsic mode functions with constant amplitudes corresponding to harmonic load excitation.

[0117] According to Equation (8), the amplitude of the correlation function of the vibration response under harmonic excitation is not affected by the damping of the pipeline system. The vibration amplitude of the correlation function is almost constant with the increase of time delay and does not change; on the contrary, the amplitude of the correlation function of the vibration response under random load excitation will show a trend of attenuation or amplification with the increase of time delay due to the influence of the pipeline system damping. Therefore, according to the different probability density function distributions of the amplitudes of the correlation functions of the vibration responses under the two excitation actions with respect to time delay, the intrinsic mode functions can be divided into two categories, that is:

[0118]

[0119] It can be understood that Equation (8) contains the set composed of intrinsic mode functions with varying amplitudes and the set

[0120] , .

[0121] wherein, and respectively represent the intrinsic mode functions with varying amplitudes and constant amplitudes, and are the amplitudes corresponding to the two types of intrinsic mode functions respectively; and are the phases corresponding to two intrinsic mode functions respectively; i = 1, 2, ……, , h = 1, 2, ……, ; and represent the numbers of two intrinsic mode functions respectively, and .

[0122] It should be emphasized that among all the obtained intrinsic mode functions, only the modal peaks with decaying amplitude characteristics are the direct manifestation of the dynamic characteristics of the pipeline system itself. Therefore, in the present invention, the intrinsic mode functions with constant amplitude caused by harmonic loads are removed, and only the intrinsic mode functions with free decay characteristics are retained to participate in the modal parameter identification calculation in the following text. The corresponding modal function set can be expressed as:

[0123]

[0124] In the formula, and are the i th natural frequency and damping ratio respectively, is the amplitude constant.

[0125] Step 4: According to the changing trend of the amplitude of the intrinsic mode function of the vibration response correlation function, distinguish the harmonic modal response caused by harmonic excitation and the structural modal response caused by broadband random excitation, and then accurately filter out the harmonic modal response to avoid the influence of harmonic false modes on the identification results of the pipeline complex modal parameters.

[0126] Step 5: Remove the intrinsic mode functions with constant amplitude, and establish an intrinsic mode function matrix; perform Hilbert transform on the intrinsic mode function matrix, and combine the intrinsic mode function matrix with its Hilbert transform matrix to obtain a signal analysis matrix.

[0127] After removing the intrinsic mode functions with constant amplitude, substitute the intrinsic mode components with variable amplitude at all measuring points of the pipeline into Equation (10) to establish an intrinsic mode matrix of the pipeline vibration response.

[0128] (10)

[0129] In the formula, represents the intrinsic mode function matrix.

[0130] Perform Hilbert transform on Y(T), and combine the original signal matrix Y(T) with its Hilbert transform matrix X(T) to obtain a signal analysis matrix Z(T).

[0131] (11)

[0132] Wherein, Z(T) is the signal analysis matrix, Y(T) is the intrinsic mode function matrix, and X(T) is the matrix obtained by performing Hilbert transform on the intrinsic mode function matrix.

[0133] Step Six: Based on the signal analysis matrix, identify the amplitude and phase of the complex modal vibration mode of the current-carrying pipeline, as well as the natural frequency and damping ratio of the current-carrying pipeline.

[0134] The amplitude matrix of the signal analysis matrix is expressed as follows:

[0135]

[0136] The phase matrix of the signal analysis matrix is expressed as follows:

[0137]

[0138] If the q degree of freedom on the pipeline is used as the reference point, the amplitude matrix of the complex modal vibration mode of the pipeline can be obtained through the following formula:

[0139]

[0140] Wherein, represents the amplitude matrix of the complex modal vibration mode of the current-carrying pipeline, and all elements in its q th row are 1; represents the amplitude of the p th degree of freedom on the current-carrying pipeline and the i th order modal vibration mode; is the constructed amplitude modulation matrix, expressed as:

[0141]

[0142] Correspondingly, if the q degree of freedom on the pipeline is used as the reference point, the phase matrix of the complex modal vibration mode of the current-carrying pipeline is:

[0143]

[0144] Wherein, represents the phase matrix of the complex modal vibration mode of the current-carrying pipeline, and all elements in its q th row are 0; represents the phase angle of the p th degree of freedom on the current-carrying pipeline and the i th order modal vibration mode; is the constructed phase modulation matrix, expressed as:

[0145]

[0146] The complex modal vibration mode of the current-carrying pipeline can be expressed as:

[0147]

[0148] Reference point q Both the logarithmic amplitude and phase of the eigenmode component of the autocorrelation function of the vibration response are linear functions of time and can be expressed as:

[0149]

[0150] Wherein, is the element in the i th row and i th column of the amplitude modulation matrix Λ, is the i th damping ratio, is the i th natural frequency, T is the time delay, is the amplitude constant of the element in the q th row and i th column of the matrix, is the i th modal instantaneous phase, is the i th modal frequency, is the reference point q phase difference of the autocorrelation function of the vibration response at frequency , and respectively represent the slopes of the logarithmic amplitude-time curve and phase-time curve of the i th eigenmode component; and are constants, and they can be obtained by linearly fitting and with respect to the time delay T by the linear least squares method.

[0151] The i th natural frequency and i th damping ratio of the current-carrying pipeline can be expressed as:

[0152]

[0153] Obviously, the complex modal parameters of the current-carrying pipeline in the operating state can be identified through Eqs. (14), (16) and (20).

[0154] That is, step six can effectively identify the amplitude and phase of the complex modal vibration mode of the current-carrying pipeline, solve the problem that the identification result of the complex modal vibration mode of the pipeline is inaccurate due to the accumulation of numerical errors, and can accurately identify the natural frequency and damping ratio of the current-carrying pipeline.

[0155] In particular, due to the interference of test noise and errors, the identified complex modal vibration mode amplitudes and phases may be time-varying. In this case, the noise interference can be removed by linear regression method to obtain time-invariant complex modal amplitudes and phases.

[0156] In summary, Embodiment 1 provides a method for identifying complex modal parameters of a current-carrying pipeline under harmonic excitation and broadband random excitation. By introducing variational mode decomposition, the correlation function of the pipeline vibration response is decomposed into a series of independent eigenmode components. Then, according to the characteristics of the constant amplitudes of the eigenmode components of the vibration response correlation function under harmonic excitation given by the following formula (8) and the characteristics of the variable amplitudes of the eigenmode components of the vibration response correlation function under broadband random excitation, the structural modal response of the pipeline and the spurious modal response caused by harmonic loads are distinguished, and the eigenmode components of the vibration response correlation function under harmonic excitation are removed accordingly, only retaining the eigenmode components of the vibration response correlation function under broadband random excitation, thus solving the problem of spurious modes in the identification of complex modal parameters during the operation of the current-carrying pipeline. By using the Hilbert transform to analyze the eigenmode matrix under random excitation, and then separately identifying the amplitudes and phases of the complex modal vibration modes of the current-carrying pipeline according to formulas (14) and (16), it avoids the influence of the accumulation of relatively large real part identification errors on the identification results of relatively small imaginary parts during the simultaneous identification of the real and imaginary parts of the traditional complex modal vibration mode, and increases the accuracy of the identification results of the complex modal vibration mode.

[0157] Embodiment 2:

[0158] Embodiment 2 provides a system for identifying complex modal parameters of a current-carrying pipeline, including:

[0159] A vibration response acquisition module, configured to acquire the vibration responses of a plurality of measurement points on the current-carrying pipeline under load excitation;

[0160] A correlation function calculation module, configured to select a reference point and calculate the vibration response correlation functions of each measurement point and the reference point;

[0161] A variational mode decomposition module, configured to use variational mode decomposition to decompose the vibration response correlation function under the combined excitation of harmonic loads and random loads into a series of independent eigenmode functions;

[0162] A classification module, configured to classify the eigenmode functions into two categories: eigenmode functions with variable amplitudes corresponding to random load excitation and eigenmode functions with constant amplitudes corresponding to harmonic load excitation;

[0163] A matrix construction module, configured to remove the eigenmode functions with constant amplitudes, establish an eigenmode function matrix; and perform a Hilbert transform on the eigenmode function matrix, and combine the eigenmode function matrix with its Hilbert transform matrix to obtain a signal analysis matrix;

[0164] An identification module, configured to identify the amplitude and phase of the complex modal vibration mode of the current-carrying pipeline, as well as the natural frequency and damping ratio of the current-carrying pipeline, based on a signal analysis matrix.

[0165] The current-carrying pipeline complex modal parameter identification system provided in Embodiment 2 is used to perform the steps in the current-carrying pipeline complex modal parameter identification method described in Embodiment 1.

[0166] Since the functions of the modules in the current-carrying pipeline complex modal parameter identification system provided in Embodiment 2 correspond to the steps in the current-carrying pipeline complex modal parameter identification method provided in Embodiment 1, reference can be made to the description in Embodiment 1 for understanding, and details will not be repeated here.

[0167] Finally, it should be noted that the above specific embodiments are only used to illustrate the technical solutions of the present invention and not to limit them. Although the present invention has been described in detail with reference to the examples, those of ordinary skill in the art should understand that the technical solutions of the present invention can be modified or equivalently replaced without departing from the spirit and scope of the technical solutions of the present invention, and they should all be covered within the scope of the claims of the present invention.

Claims

1. A method for identifying the complex modal parameters of a current-carrying pipeline, characterized in that, It includes the following steps: Obtain the vibration responses of several measuring points on the current-carrying pipeline under load excitation; Select a reference point and calculate the correlation function of the vibration responses between each measuring point and the reference point; Using variational mode decomposition, decompose the correlation function of the vibration response under the combined excitation of harmonic load and random load into a series of independent intrinsic mode functions; Classify the intrinsic mode functions into two categories: intrinsic mode functions with varying amplitudes corresponding to random load excitation and intrinsic mode functions with constant amplitudes corresponding to harmonic load excitation; Eliminate the intrinsic mode functions with constant amplitudes and establish an intrinsic mode function matrix; perform Hilbert transform on the intrinsic mode function matrix, and combine the intrinsic mode function matrix with its Hilbert transform matrix to obtain a signal analysis matrix; Based on the signal analysis matrix, identify the amplitudes and phases of the complex modal shapes of the current-carrying pipeline, as well as the natural frequencies and damping ratios of the current-carrying pipeline; Among them, the element in the p -th row and i -th column of the intrinsic mode function matrix is expressed as: In the formula, is the element in the p -th row and i -th column of the intrinsic mode function matrix, p = 1, 2, …, , is the total number of measurement points, i = 1, 2, …, , is the number of intrinsic mode functions with varying amplitudes; q represents the reference point; The element in the p -th row and i -th column of the signal analysis matrix is expressed as: Among them, ; In the formula, is the element in the p th row and i th column of the signal analysis matrix; In the expressions of the intrinsic mode function matrix and the signal analysis matrix, is the amplitude of the element in the p -th row and the i -th column of the matrix, is the amplitude constant of the element in the p -th row and the i -th column of the matrix, is the i -th order damping ratio, is the i -th order natural frequency, T is the time delay, is the phase of the element in the p -th row and the i -th column of the matrix; Among them, , is the i th-order modal frequency; is the phase difference between the p degree of freedom q and the vibration response correlation function at the frequency .

2. The method for identifying the complex modal parameters of the current-carrying pipeline according to claim 1, characterized in that By arranging velocity sensors or acceleration sensors on the current-carrying pipeline, test and obtain the vibration responses of the measuring points under load excitation.

3. The method for identifying the complex modal parameters of a current-carrying pipeline according to claim 1, wherein Select the measuring points on the current-carrying pipeline whose vibration responses are greater than the first threshold and the number of modal peaks is greater than the second threshold as the reference points.

4. The method for identifying the complex modal parameters of a current-carrying pipeline according to claim 1, characterized in that The variational mode decomposition decomposes the correlation function of the vibration response into a superposition of a series of amplitude-modulated and frequency-modulated signals. The variational mode decomposition establishes a constrained variational problem, transforms the constrained variational problem into an unconstrained variational problem through an augmented Lagrangian function, and uses the multiplicative operator alternating direction method to solve for the optimal solution to obtain the intrinsic mode functions and their corresponding central frequencies.

5. The method for identifying the complex modal parameters of the current-carrying pipeline according to claim 4, characterized in that, After each iteration update of the intrinsic mode functions and the central frequencies, first update the Lagrangian multiplier operator, and then continue to execute the iteration until the convergence condition is satisfied.

6. The method for identifying the complex modal parameters of a current-carrying pipeline according to claim 1, wherein, The set composed of intrinsic mode functions with varying amplitudes is denoted as: ; Among them, ; In the formula, is the i th intrinsic mode function with a varying amplitude, is the amplitude of the i th intrinsic mode function with a varying amplitude, is the amplitude constant of the i th intrinsic mode function with a varying amplitude, is the i th damping ratio, is the i th natural frequency, T is the time delay, is the i th phase of the intrinsic mode function with a varying amplitude, p represents the measurement point, q represents the reference point, i = 1, 2, ……, , is the number of intrinsic mode functions with a varying amplitude; The set composed of the intrinsic mode functions with a constant amplitude is denoted as: : Among them, ; wherein, is the h th intrinsic mode function with a constant amplitude, is the amplitude of the h th intrinsic mode function with a constant amplitude, is the phase of the h th intrinsic mode function with a constant amplitude, h = 1, 2, ……, , is the number of intrinsic mode functions with a constant amplitude, , K is the total number of intrinsic mode functions.

7. The method for identifying the complex modal parameters of the current-carrying pipeline according to claim 1, characterized in that The complex modal shape of the current-carrying pipeline is expressed as: In the formula, is the complex modal vibration mode of the current-carrying pipeline, is the amplitude matrix of the complex modal vibration mode of the current-carrying pipeline, is the phase matrix of the complex modal vibration mode of the current-carrying pipeline; Taking q the degree of freedom as the reference point, we obtain the element in the p th i row and th column of q is expressed as: and all elements in the q th row are 1; Taking q the degree of freedom as the reference point, we obtain the element in the p th row and i th column of is expressed as: and all elements in the q th row of are all 0; In the formula, is the element in the p th row and i th column of p and represents the amplitude of the i th order modal vibration mode of the th degree of freedom on the current-carrying pipeline; q is the amplitude constant of the element in the i th row and th column of the matrix; is the element in the p th row and i th column, representing the phase of the p th degree of freedom of the i th order modal vibration mode; is the reference point q the phase difference of the autocorrelation function of the vibration response at the frequency .

8. The method for identifying the complex modal parameters of the current-carrying pipeline according to claim 1, wherein If the amplitudes and phases of the complex modal shapes of the current-carrying pipeline identified based on the signal analysis matrix are time-varying, then process them through a linear regression method to obtain the amplitudes and phases of the time-invariant complex modal shapes.

9. A complex modal parameter identification system for current-carrying pipelines, characterized in that It includes: A vibration response acquisition module for obtaining the vibration responses of several measuring points on the current-carrying pipeline under load excitation; A correlation function calculation module for selecting a reference point and calculating the correlation function of the vibration responses between each measuring point and the reference point; A variational mode decomposition module for using variational mode decomposition to decompose the correlation function of the vibration response under the combined excitation of harmonic load and random load into a series of independent intrinsic mode functions; A classification module for classifying the intrinsic mode functions into two categories: intrinsic mode functions with varying amplitudes corresponding to random load excitation and intrinsic mode functions with constant amplitudes corresponding to harmonic load excitation; A matrix construction module for eliminating the intrinsic mode functions with constant amplitudes and establishing an intrinsic mode function matrix; and for performing Hilbert transform on the intrinsic mode function matrix and combining the intrinsic mode function matrix with its Hilbert transform matrix to obtain a signal analysis matrix; An identification module for identifying the amplitudes and phases of the complex modal shapes of the current-carrying pipeline, as well as the natural frequencies and damping ratios of the current-carrying pipeline, based on the signal analysis matrix; The current-carrying pipeline complex modal parameter identification system is used to execute the steps in the current-carrying pipeline complex modal parameter identification method described in any one of claims 1-8.

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